Evite is willing to sacrifice security for usability. Which makes sense, because it doesn't really matter if someone hacks your Evite account.
But, the onus here should really be on the user. If they are careless enough to use the same password for everything, they are indicating that they are willing to trade some security for convenience. In my opinion, emailing users their password is just another security/convenience trade-off. I'd be upset to get my password sent in plantext from my bank, but not an invite website.