I think I would give them a miss then as I do not want a blackbox in my car either. My advice would be do to the search again and rng up Tesco's car insurance directly and give them the quotes that she has recieved and do not be afraid to leave.
I was with Admiral before and they matched prices for a good number of years and then last year they could not match the price I had when I spoke to them and then I left, but I made sure that I had I phoned the company up, to finish the quote. I always do this, and I mention that I had truouble completing it online and transaction did not go through. To be fair then I get them to go through the quote and information with me that I put in and they match virtual match the price online, sometimes it has been£10 higher others a little bit lower, but at least I know the information I have submitted is correct. I am not good on the computers