It is also partly your friend's mistake. These things should be in writing for many reasons - - the recruiter could just possibly lie that she never mentioned

It is also partly your friend's mistake. These things should be in writing for many reasons - - the recruiter could just possibly lie that she never mentioned remote work - the recruiter could have left the company and could possibly never answer your messages - the doc would stand as a point of argument with the company without involving another person into the discussion