lol. i don't like anything about that setup. im sure its fine

hi,  i use thishttps://www.festoolownersgroup.com/festool-how-to/how-to-use-copier-scanning-set/

I am sure I have done it at some point early on before there were good rabbeting bits with ball bearing pilots. I do not see any reason to do it now.

If it goes off the edge guide a bit while pushing forward it looks to me like it would jam and make the router scoot across the room. 

I wouldn't be that bold as to make that statement...that's what those massive biceps are for.   
Besides, it's all about mechanical advantage/leverage and a small 1/2" diameter router bit will not be capable of propelling a 9# router across the room. It could, if not controlled leave a nasty divot in the wood, and that would be unfortunate but it has been done this way in a pinch many times before

Just remember, if you're uncomfortable with the routing method that you're using, then maybe it's time to rethink the methodology you're using.

doesnt look very safe, and as others pointed out, i would have used a bearing bit.

There are several issues here as most have pointed out. The trapped cut though, is the least of them as I see it. A trapped cut like that on a solidly held, single piece, that is made in the "conventional cut" direction and a light cut, would be somewhat acceptable. Not ideal, there are better ways, but it would work.
The problems the I really see here are far more severe.
First is the inside cut of an enclosed space. The is no way to start this cut "off the work" when it is internal like that, other than plunging straight down, not good.

Second is the closed space itself. What do they think is going to happen when you get to the corners?

Third is the fence itself. Those have a opening that is intended to straddle the bit, much like a router table. They work just fine when doing that, but if you have any more off-set than that, you need to attach a single piece to span that gap. The router will "fall into" that gap when it gets to the end. At minimum this spoils the cut, and worse may injure the user and or tool too.
These fences, from all brands, have holes in them intended for screws to hold on and auxiliary face to solve this issue.
The nicer brands (Festool) have sliding parts to accomplish this same goal.

Either way, this is lousy advertising. Someone should have seen that this was bad and definitely not the intended use of this edge guide. Normally they are hyper-vigilant about safety things and warnings that pretty much anyone already knows, or wouldn't do anyway. They all give warnings that people read and say "well that's silly" or "who would do that?"

I am truly surprised that this image appeared on the Woodpeck.com site
at all, unless it was to show an unsafe method of using a trim router.

What was this image intended to illustrate? I don't see a Woodpeckers
product in the photo which is what makes me question it's use.

Edit: found it.
https://www.woodpeck.com/blog/stylish-bathroom-vanity.html

Snip.
Edit: found it.
https://www.woodpeck.com/blog/stylish-bathroom-vanity.html

So the unsafe router use was actually made by someone who shared his project on WP's site, not by a WP staff member. Not sure if the site contains any of the usual "No responsibility" or "Use at your own risk" disclaimers.

It appears that what is most important is that every photo, where possible,  has to include at least one red Woodpeckers' product. 

Only two photos fail in that regard.

That chatter is actually tearout from cutting the wrong direction. This is especially bad with splintery species like Oak and hickory, but having the cutter exit on unsupported material will do this.
A very shallow climb-cut, similar to how dovetails are cut with a jig, is the best way to avoid this kind of tearout. Many people are sketched out by climb cuts too though.
Personally, I would rather see this done before assembly, on a router table, but you can't always have that "best case scenario".

Before the plunge router was invented, old folks angled their routers to start such a cut.

I have to cut a ¼" wide x ¼" deep groove centered on the face of a cabinet door frame that is 3½" wide x ¾" thick.  I need the groove for the spline on a wicker door front.  It has to go entirely around the frame.

I was planning on doing this on the table mounted router and using the fence for a guide.  I would mark the two edges of the router bit on the fence and make marks for the location of the grooves on the work-piece.  I would guide the door frame until I approach the marks on the fence.  I would clean up the corners with a chisel.

Any thoughts on that approach?

The complication, which I did not mention, is that the door frame is already painted.  I will be using a down cutting Whiteside bit, which should eliminate any tear-out. 

I will also allow the paint a couple of weeks to cure and I will use the easy-release yellow Frog tape to protect the area not to be cut. 

After I get that all done, I have to apply the cane webbing without screwing up all that went before it.  And this is all new to me. 

The inspiration was this cabinet from Pottery Barn.  All the cabinets in the bathroom were emerald green, and I wanted to break that up.  The cane center panel seemed like a good way to do this. 


https://www.potterybarn.com/products/dolores-cane-cabinet-buffet-mp/

The complication, which I did not mention, is that the door frame is already painted.  I will be using a down cutting Whiteside bit, which should eliminate any tear-out.  Snip.

Tape as Tsmi suggested would help but not foolproof as paint/wood fibre can still tear. If I were doing such a delicate cut with only one-take, I'd do this:

- Put tape on the cutline area
- Scribe on the tape/wood with a sharp marking gauge (scribe in three strokes: light, med & heavy) to mark off the good and waste side. If you aren't familiar with the three-stroke technique, practice it on a scrap). A deep incised line will prevent tearing off the paint.
- Set the plunge fence so the cutting edge of the bit is on the waste side
- Make multiple passes, not one heavy pass to remove the waste.

You can actually run through the whole thing on a scrap (unpainted or painted).

I wouldn't do it using a router table though as it's much harder to set/position the fence precisely.

How big are these doors? Especially in comparison to your router table's fence.
I think, at first thought, that I would do it one the table, with stops.
It would take two set-ups, assuming that the doors are not square.
Using a test piece of the same size, set a start and stop position, using stops clamped to the fence or table. Run those edges. Then change the set-up (stops) to the length of the other sides, so they meet the previous grooves in the corners. No guessing, no slow-downs hoping to hit it close enough, chisel the corners, done.
The fact that the parts are pre-painted is unfortunate. It poses some risk, either way, above or below.
I have had mixed results with tape. Sometimes it works fine, other times it catches or snags, which is a problem. It can make things worse.