Where did the spoke break? Near the nipple or hub or in the middle?

No way your rack/pannier are causing a broken spoke on their own. I'd say the wheels already had a spoke issue or that the bike shop improperly trued the wheel. Ask around for a different shop that does a lot of wheel work and take it there and see if you get a better result.

FWIW, I weigh 185 lbs and commute with a rack/loaded pannier that probably adds another 15-20 lbs. to the total weight. I commute on 24 spoke wheels and have not broken a spoke in 17,000+ miles of commuting over the last three years. I am not particlarly gentle with the wheels either. I don't abuse them, but have no problem popping up or down a curb and ride over some crappy roads.