Rear fenders help bottom brackets a lot, both from direct spray (and this spray is dirtier than the spray from the front wheel which is passing through undisturbed water) and possibly down the seat tube. Front fenders, if they have deep flaps, protect the bottom bracket from about 90% water it would otherwise see. Full fenders with the front having a deep flap will make a huge difference.

I make deep flaps for all the fenders I buy. Most non-English fenders come without. Some like Planet Bike had front flaps that are just toys. I remove them and put real ones on. There are now a few fenders out there with good flaps. Cascadias by Planet Bike for one. There are also retro-fit flaps to be had. (I find this all a little amusing. In the '60s, Blummel of England was virtually the only choice. They came with deep, very effective flaps.)

IF you are happy paying the bike shop for their work, they should not be scolding you. If you come in complaining about the short life of your bottom brackets and they have been telling you for a while to get fenders, you deserve what they are saying.

Ben