I put hired car which is perfectly acceptable in English UK but it was rejected
Well I have reported it sometimes, can't remember when. I am under the impression that DUO has technical difficulties to correct this. There are other threads about similar problems. It has to do with the audio engine. In some cases they might be better off just use audio recordings IMHO. Let's wait and see.
I am a native English speaker and no, that would be incorrect because you "rent" a rental car, you don't "hire" it. "Rent" means to pay someone to let you borrow an item from them for a limited time. "Hire" means to pay someone for their services or to perform a task for you. Employers "hire" employees, for example. A "hire car" would be more like a taxi, because you are hiring the driver to take you somewhere, but nobody ever uses the term "hire car" for anything in English. I know this isn't an English course and I know this is a pretty late reply, but I hope it helps.