It is really hard to speculate about what might have actually happened. I understand that you decline to post the exact particulars , and that you are a "third party" which could result in something being lost in translation.
I'd love to hear the full story from "your friend". As has been pointed out before, the anti-spam conditions of the TOS may well have had as much to do with the "disablement" as the number of emails sent.
The nature of the email has a lot to do with it; I have gotten a lot of SPAM disguised as "Merry Christmas Greeting" - I'm sure you have too. I'd also like to know more about the site(s) mentioned in the email. Is it monetized in any way (adsense, etc.?).
Since you keep focusing on the "only 60 emails", I'm, wondering if you, or your friend, have considered that, since the limit is 100 per hour, the actual problem may have been that the 60 emails plus whatever other email normally goes through that server from that user might have actually been over 100.
If anything on your friend's site(s) sends email (mail a friend link, new post notifications, lost password, new user confirmation, etc.) it could very easily be that the "extra 60" pushed the actual usage over 100 per hour- that is very possible.
Again, I think you are likely focusing on the wrong issue. While I can't know for sure, as I haven't seen the DH notice or the email in question, I'm thinking it is more likely a spam issue that got DH's attention than a quota issue, or that the "total" number of email was actually over 100 (of which the "60" was a part).
If their concern was actually what they consider to be the "spammy" nature of the email, they may have indeed mentioned the number sent on that one run but, if that is the case, that shouldn't be taken to mean that the number alone is what caused the disablement.
Hopefully, by working through the issue with DH support, she will be able to get it all sorted as quickly as possible.