IS is based on a Corolla platform, GS is based on Camry, and LS is based on the Avalon. They're not independent platforms, the only Japanese car manufacturer to do that is Nissan/Infiniti. The G (Nissan Skyline in Japan) is its own platform but shares some of its drivetrain with the Z, the M (Nissan Fuga in Japan) is its own platform. The Smaller SUV is based on the G, the Mid sized SUV is based on the M, and the large SUV is based on the Nissan Armada.
I never liked the fit and finish of Lexus, the outsides looked nice but the interiors looked as cheap as a Toyota interior. Maybe its changed in the 5 years + I've looked at one.
Good luck with your issue, call Lexus I highly doubt they would condone the treatment of a potential customer like this. http://www.lexus.com/contact/ A lot of times these dealers do asshat things thinking you will never tell corporate.
I am not a lexus fan but you're also wrong. The lexus IS, GS, and LS are all rwd vehicles while the three toyotas you mentioned are FWD vehicles. Definitely not the same platform.