Yes it was a lab error. They processed traditional B&W in C41. They should have known better. Now you know. My suggestion, if you are looking for one, is to have your B&W processed by thedarkroom.com if your not doing it yourself. Not very expensive and they are good quality and fast. See their ad as an APUG sponsor.
The odd times I take a B&W film in to be developed for me (i.e. 127 size films) I make a point of saying that it is old fashioned B&W film, not colour. They then know to send it away to their central facility.
Tri X isn't really "drug store" film (who coined that term anyways? It ranks up there on the cringe list, along with nifty-fifty...)
I'm not even sure if minilabs (the machines that do C-41) handle b&w
Make sure you spec B&W film.
Conversely, if you use a C-41 B&W film, make sure they run it in C41
Frankly unless you are devoted to trad B&W film and are prepared to put up with the extra postage cost, time, potential loss in mail etc then it might makes sense to buy Ilford XP2 Super which is a B&W C41 film that is designed for printing in B&W chemistry
If you decide to go with local mini-lab printing as well which is RA4(colour) paper then it is said that the Kodak C41 equivalent is designed for RA4 paper so Kodak B&W C41 film may be the best bet.
Sorry to hear about the burnt roll.
It was a similar situation that convinced me to start developing myself. I was specifically buying BW400CN so that I could just take it to a drug store. Little by little the local places stopped developing and there was only one drug store that still did it. I dropped off a roll there and came back later to pick it up to find a lady working there completely irate with me for "ruining her machine".
When I asked what she meant, she accused me of purposely sabotaging her machine by not telling her it was black & white film and it had turned the machine into a sticky mess, mangling and destroying my film and causing some sort of unspecific mayhem within the machine as well.
After she was done, I grabbed a box of BW400CN from the rack beside her and showed her that it specifically said it was meant for normal process, even though it was black & white, so it couldn't have been my film. In response she didn't apologize, offer me a free roll of film or anything other than asking me to leave the store.