In any case, I try to always write in full sentences for professional communications as a minimum (even if there are sprinkles of informal language)—I'm more comfortable writing this way at work, and it has the added benefit that it's hard for a third party to make a similar comment like you've experienced.
(At the other end, it can also be seen as too stiff and uncomfortable to be overly formal, even to supervisors. I've seen this where I had a direct report who was excessively formal at first. By encouraging him to open up and speak more openly, I believe that created a foundation for a more trusting work environment over time, which encouraged him to take more initiative and share his ideas when solving some problems that we were later facing as a team.)