Fixes#9351.
Note that this commit reworks that fix for #9317. The change
is to check that the type implements `AsRef<str>` before regarding
`to_string` as an equivalent of `to_owned`. This was suggested
by Jarcho in the #9317 issue comments.
The benefit of this is that it moves some complexity out of
`check_other_call_arg` and simplifies the module as a whole.
