I don't believe there are strict/written rules on the subject, and below is nothing more than just my experience and opinion.
Is that we should not contact users and moderators directly, unless there is a good reason to make an exception to the rule.
Having said that
I have both been contacted by users (and once a moderator, not for suspension :) ), and I have contacted users and moderators occasionally. I must say I never felt I was offended, nor by the nature of the message, nor by the fact that they contacted me.
Likewise, I never felt that I did anything wrong in contacting people, especially if their email address is in their profile or the first link in the profile brings me to their email address. I can only hope they didn't feel offended, like I didn't feel I was.
At the same time, As said, I don't believe you can or should just contact anyone outside the site, and we should respect privacy and the fact that people might very well want to separate their daily life from their presence on AU or SE in general. This counts even more on moderators, since their position is more vulnerable by nature.
What I feel is especially inappropriate
- Discussing moderation decisions, no matter if it is moderation by users (like your example), or by a moderator. These discussions belong on the site, either in chat or on meta.
- Discussing answers, or giving support on questions that belongs on the site. This is leading away the discussion from the place where we all benefit from given insights.
- Just contacting people for "chatty" reasons, with no reason(s) that justify making an exception on the rule.
No doubt the list is incomplete, but these are the most important ones I guess.
In short, in this case
I would say it is inappropriate for anyone to contact you about moderation. The fact that it is not an offensive message doesn't change that. Moderation and the discussion about that belongs on the site.