Bobwax- I've dealt with this many times, starting back in the '70s, and as noted it's hard to do a permanent fix. So hard that I'd expect a (honest) shop to warn you that their repair probably won't last. I have had this work out OK, both jobs done by Pros and jobs I've done myself, but the successes are a small percentage of the attempts and even with the best work and the best products, IME it's simply a crapshoot.
Hint#1: Some of the newer "paint over rust" products are much better than the old standbys like POR15, and those can make for *great* primers when doing this type of work. Don't stop at three coats. If topcoating, I'd do it *without* sanding because that sometimes compromises the paint over rust product. Yeah, that can pose problems, but IMO how it looks isn't as important as keeping it rust-free.
Hint#2: do the same rust remediation/paint-over-rust priming/etc. on the inside of the doors too; get those seams totally sealed up with the stuff.
Hint#3: rustproof the repaired seams from inside the door with something that'll wick into the entire area in question *without leaving any gaps or pockets*. That last bit is utterly critical and IME determines which products to use for this. If using a pro undercoating gun, I'd use ValuGard's product, but I have *NOT* done all that well with their aerosol version. Yeah, probably "user error" but I'm not the dullest tool in the shed (note that I learned rustproofing from a very experienced pro and I'm quite meticulous about how I do such stuff) so if it's not Accumulator-proof then I can't recommend it. Likewise, my usual fave rustproofing (at least for areas that show), Eastwoods' Black Heavy Duty Anti-Rust, just doesn't wick well enough for this application IME. (Ditto for the Wurth products I've tried.) The aerosol stuff that *has* worked OK for me is Cavity Coater by KBS (who also sell some very good "paint over rust" products and a *GREAT* industrial-type clear). Same ol' same ol'...don't stop after just a coat or two.