Ok - I'll give a somewhat different view on this.
DH and I met through OLD a few years after my D. He wanted to meet right way - I wanted to know more about him before we decided to meet. I'd had a wide range of experiences with OLD, and wanted to have more information before we met to try and match up with the reality once we did meet... looking for ways to "test" how honest he was.
I was putting a kind of high bar on getting past the on-line chat to meeting in person, because I saw the kind of guys I was meeting when I jumped right into the first in-person meet. Nothing too bad, nothing dangerous - but enough "off" behavior that I started getting concerned about it. In fact, when I started talking to DH, I had all but given up OLD... I almost didn't contact him back, and really hadn't planned on trying to start any relationships right then.
now-DH started to push to meet pretty quickly after we started communication on-line. He was understanding when I put him off, but he did keep pushing some to meet too. I would write long e-mails with lots of questions. He would write back short e-mails which did answer the questions I asked, but which tended to be very short answers that didn't go into much detail. He might ask a few things back of me, but not much.
Honestly, I'm still surprised sometimes that I actually went forward with meeting him. There was something there in even those short answers, I guess. Also, I was impressed that he DID persist. If figured if he was one of the ones looking to do anything weird, he would just move on rather than put in the time with me.
In talking about it all later, I got his side of it. He was pushing to meet more quickly because he'd had WAY too many experiences with women who said they wanted a relationship, only to find that either they weren't ready, or weren't over someone else, or there was no chemistry on one side or the other once they finally met. He had decided it wasn't worth weeks/months of time just to have it be a complete non-starter at the first meeting.
And as far as the really short answers/not really giving much back in the e-mail exchange? He ended up telling me that he had been somewhat intimidated by how much I could write back to him so quickly. He is not a very good typist, and has no patience for sitting and typing out long prose the way I can (confirmed by this message, I'm sure!) He has no trouble communicating, and we talk a lot about everything - did pretty much from the first time we met. But it took him a LOT longer than it did me to type things out, and it was just something he isn't very good at.
I'm not saying to not pay attention to things that are "flags" for you. But for a lot of these things, there's more than one explanation. And it really is difficult to tell about a person without meeting in person first.
Take it for what it's worth. There's no good answer to it. You just kind of have to go with your gut, and make sure as you go along that you do the "girlfriend test". (That's where you ask yourself what advice you would give a girlfriend if she were in your situation. And you answer it honestly.)
ETA: I should have added in there that some people are not "phone conversation" people. I'm one of them. Of course, I don't do texts either. My point is that he might just not be willing to invest much until you meet in person - much like my DH wasn't.