Maybe I got the single bad apple, but one of the ladies there asserted that I MUST charge the rental to my corporate credit card in order to get the LDW.

I was renting for personal reasons on my personal credit card (which our company contract DOES allow and should always include the LDW).

I ended up going with what the lady said. I charged it to my corporate card in my profile. At the return, different lady changed it back to my personal card. A bit of an inconvenience, but not terrifying.