They might well be telling the truth by accident.
Google Groups specifically is notorious for hosting malware, phishing, and spam, and Google won’t do anything about dealing with the abuse because 1) cleaning up abuse is not a profit center, 2) they’re Google - who would dare to block them? Over the years I’ve seen several good sincere people at Google with impressive tech credentials go into that mess to clean it up and eventually give up in frustration because nobody else at Google gives a shit about it. The Google blog services they bought - Blogspot, etc. - have similar issues, plus a tendency to make arbitrary, capricious, and downright crazy judgements against ordinary users.
