You're absolutely not being over the top. I've had endless problems with school catering, but fortunately was able to choose to send them in with packed lunches instead.
Now FS and KS1 get free lunches, dd wants to be the same as her friends and has started school meals again. She has Vegetarian, no meat or fish and then NO FISH entered on her record, against which her meals are supposed to be checked before she eats them, yet she was still given a fishcake a couple of weeks ago. Fortunately, despite being only 6 years old, she knows exactly what a vegetarian is and didn't eat it. It isn't the first time they've tried to give her fish either, with certain kitchen staff insisting vegetarians eat fish. 
Obviously she's in primary, so the complaint pathway is a little different, but I sent a strongly worded letter to her form teacher, who arranged for her to be taken to visit the kitchens, meet the head cook and be introduced to all the catering staff, so that they know her by sight and will not attempt to give her non-vegetarian food again. She also spent time with the lady that checks the food out on the system to be sure she can't overlook dd's dietary requirements again in future. The head cook took it very seriously, was very apologetic and assured me that systems would be really tightened up to make sure it can't ever happen again.
When ds1 was younger he had a stand up row in the classroom with his y1 teacher, because she insisted all vegetarians eat fish. He has ASD and there was no way he would back down, so it was reported to me. I was then in trouble for backing his point, if not his way of getting it across. The teacher concerned still wouldn't agree with me and said we should agree to disagree. 
When he was 7 he had a raft of tests and we were told by his paediatrician that he is not to eat gluten. He now has compulsory hot meals at his secondary school and they've been great, creating a separate menu of meals he really likes especially for him, but he regularly gets symptoms of having been 'glutened' and I'm pretty sure that will be from cross-contamination - as in using the same oil as the normal lunches to cook his food in.
Avoiding cross-contamination between meat and vegetables (and gluten and coeliac safe foods) is basic kitchen hygiene and anyone with any sense knows not to cook vegetarian and non-vegetarian in the same pans/oil or use the same chopping board etc. As Alpaca said, I would be seriously concerned about their general food hygiene practises (sp?) and suspect they are just as bad with food allergies. Not good enough at all.
Apart from the fact that they've done it, they had absolutely no right to quiz your daughter about whether she checks how food is prepared in every restaurant and take-away she goes to. Talk about putting her on the spot, how intimidating. 
I don't think you'd be being unreasonable to send in a strongly worded letter explaining that dd will be bringing her lunch from home until such time as the catering team can satisfactorily reassure you that they are able to provide a true vegetarian meal.