I've run across one SQE with Chrysler, though he was a contract guy, but he was great to work with. He pretty much mocked the way most of the other SQEs deal with suppliers. He told me he wasn't about getting in people's faces and degrading them, after all we are all here for the same reason. All the while he was at our facility from 3p - 11p due to a major issue with one of our suppliers.
Unfortunately the guy we usually dealt with was an arrogant prick.
I had an opportunity to work as a SQE with Mercedes about 8 months ago but turned it down. My main concern was the turnover at OEMs in such a role.