There may be somewhat of a valid concern with safety, but not really with liability as I understand it. I just think it's a bit of a shame. The initial meeting could be in a public place; in fact that's generally the rule with us when meeting new people.
A safety issue for the users is a liability issue for the owners.
What's the source of your belief? Just a guess based on your common sense? I'm curious. I still think they should add the feature.
A couple of non-child-specific analogues are craigslist and freecycle. Both appear to work just fine, by leaving details of meetups to individuals. IIRC both do post disclaimers, but I've seen nothing that indicates to me that even those are legally necessary to avoid liability. It is of course a good thing to do in light of the gullibility of some people; some really might invite strangers, sight unseen, into their homes.
Here's a website that seems to be based on the idea:
http://www.myplaydate.com/ I can't tell if the rules would require them verifying that you have a child somehow-- I doubt their ability to do that easily, so I doubt it is implemented that way-- and can't tell whether the lack of content is because I don't have a login. But their release language is pretty general, just mentioning once that they're not responsible for the behavior of members off the site, which I tend to think is common knowledge.