I notice that you posted the day of the party, so any advice about whether to turn up or not is totally moot. Your question was really whether a verbal invitation kid-to-kid is becoming the norm -- No, it's not.
Did you ask your child if possibly she was given an invitation at school by this friend and it was stuffed somewhere in her school bag? Kids this age tend to jam things into their bags, or deep into their desks, and then are convinced they gave the paper to mom or dad when they didn't. I would almost bet that if your child really was invited, there was a written invitation given much earlier and it was stuffed somewhere that you never saw it (wasn't in the backpack? Could have been inside a book, in a pencil case, whatever).
You were right not to send her. The other parents, if they did indeed invite your child, should have realized that they had no RSVP from you and contacted you to check. Unfortunately it IS now very common for parents never to RSVP and then to turn up, so the parents might have assumed that's what you were doing, but you sound like someone who would absolutely have sent an RSVP!
This has two lessons for all of us: (1) Don't invite kids unless you, the inviting parent, have solid contact information for the other parents (e-mails and phone numbers) so you can reach them if you hear nothing. (2) Don't invite kids unless you send the parents--not the invited kids--the invitation, either by snail mail or by e-mail. I would not send invitations to school to be handed out by a kid, ever. Even if the host kid hands everything out just fine, the recipients are very, very likely to mislay those papers.
If I were you I'd be sure to talk to these parents if you encounter them and say that your child mentioned a party, and if there was indeed a party that she missed, you're sorry you did not RSVP but your child never gave you an invitation and you did not have contact info.
This late in the school year, does your school not have any school directory for families to use? Or the room parent does not use e-mail to contact parents? I might have contacted the room parent, if you have one, to say that you needed to reach X's mom and dad and don't even know their names, and could the room parent give you any contact info....