My view is admittedly biased, but it seems to me that anyone who gets a doctorate (PhD) from an
online "university" is looking for some instant and convenient credibility.
So, the answer is
yes. If I had recieved my PhD online from Phoenix (or Guatemala... whatever) I would insist on being called Doctor.
Now if you are asking is this deserved... well, I..., ummm...
BTW: there is only ONE person that I insist call me Doctor. My sister! (That's DOCTOR- brother to you, sis!)
edit: I see you live IN Phoenix, Lee. My comments only apply to online university. Full disclosure: my wife is taking an online masters course in psychology at present from a bricks and mortar Canadian university, but I am quite convinced that this condensed self-study masters is not equivalent to attending classes in person.