Shitty situation. I highly doubt it’s the tires, but you have little choice now but to change them in order to prove it’s not the problem. If you do, tell them you’re keeping the old ones to put back on if they’re wrong. I had a shifting issue at one point that my dealer claimed was related to the tires. It wasn’t until the car started taking five seconds to shift into reverse that they acquiesced and replaced the trans.