When I arrived at the dealership, the service adviser they assigned to me was was a nice lady, but she also mentioned that it should be covered under warranty unless they found chewed wires by a mouse or something. I find this odd that two service advisers mentioned the same reason that the warranty might not possibility be honored.
Even though it initially sounds like they are trying to set it up to not be covered it is probably that they have just run into that issue in the past and if the customer thinks that their problem is 100% guaranteed to be covered for free right from the start it probably creates some drama when they have to explain to them later that it isn't. Dealers get paid for warranty work so they like it too. (it is what kept the domestic dealers in business for all those years)
I know it's a new model and there are usually bugs that need to be ironed out,
Even with well established car models with great reliability histories there will still be the occasional defect in a component.
I think I rather have the car replaced than have to deal with transmission issues after the warranty expires, especially since the car is so new. Am I crazy?
I wouldn't think you'd get any car company to replace a 10 month old car under warranty for the transmission going. With the OP's 3 day old car I might have tried for that.
If you had turned off your engine for a little bit then turned it back on, it may have been fine. This seems to be an annoying, intermittent problem with the tranny.
Did the tow truck driver drive the car once he got there at all? Any indication the problem was still there at that point or did he just winch it up?