You clearly have no idea how Thailand operates. There is no consistency. Whereas a tourist visa holder may find it next to impossible to open a bank account, a DTV holder might have a different experience.
What you're saying is nonsense. It's up to the branch and each individual you ask will say something different based on what they believe to be correct. Nothing to do with "saving face". What a nonsensical assumption on your part.
Cars not in your name can be taken to Laos as well with a letter of authorization. However, generally, rental car companies won't issue this letter (in rare cases they might). You can also self-drive a rental car in Laos, visit Avis. I know the general manager and founder of the company. Their cars are allowed to be driven into Thailand.
They will if it's a country, which doesn't stamp your passport anymore and there are an increasing number of those. Try Hong Kong, Singapore, Malaysia if using the autogates, even Cambodia (if arriving by air).