I've come across the period-as-negative idea before. I communicate in text media to audiences ranging from people in their early twenties to several decades my senior. I strive to communicate similarly to all. This includes capitalization and punctuation. I've discussed the negative period with several folks in this range, and none indicate that they view my communication as abrupt, brief, or negative, but that they do sometimes notice that with others.

I ultimately come to this conclusion. A period is a tiny piece of a message. If something so small makes your message seem in some way negative, then your communication is already on the margin. You should look at other areas of your communication to improve.

My default view of messages in what seems quickly to be becoming the common text style (all lower-case with abbreviations and no punctuation, written in fits of stream-of-consciousness) expresses laziness and a sense of self-importance on the part of the author. I find that assuming good intentions of the author is a much better stance to take. Thus, I choose to interpret positively what might otherwise seem negative to me. If someone else is incapable of looking past a period, then my communication must be very poor indeed, and I must make efforts to improve it.