Shwa (pronunciation)

Hello,

I have checked a few online dictionaries for this word. They all claim 'shwa' rhymes with 'bar', 'car', etc.

On the other hand, I remember hearing a native BrEng speaker (= one of the innumerable 'English learning' videos on the internet) rhyme 'shwa' with 'war'... Am I in left field with this guess?

Looking forward to you comments!