Looks like the code uses:
javax.mail.Message.isMimeType("text/html")
So it's relying on the MIME type of the email to be set correctly. Sounds like you got an incorrectly formatted email, so the only workaround I see is checking the contents manually.
Something else to think about: when displaying html from an external source you open yourself up to attacks from malicious code inside this html. So it seems to be worth to at least try sanitising the html using antisamy before displaying it.
On the original question; interesting that there would still be email clients nowadays doing this wrong. I guess manually checking the content for any html tags will provide a workaround 95% of the time.