I disagree. Common courtesy is RSVPing--which all of the girls did. I have never heard that an in person RSPV if you see the party host (the DD in this case) is not acceptable and you MUST call the number. That is just silly. If the mom felt she needed to speak with parents herself then she should have included on the invite that she would like a personal call from each parent to clarify logistics before the trip or something to that effect.
My kids are 14 and 12. All RSVPs for the last 3-4 birthday parties went through the kids with the exception of one parent who had to work on a Sunday and emailed me to see if her son could stay later (no problem). This is one of those many little things you hand over to your kids so that by the time they are adults they have had everything handed over to them and know how to function without you.
The situation you describe at your party shows poor manners on the part of invitees. The OP's situation does not. Again, all of the girls RSVPd directly to the OPs DD.
do you honestly think the teens couldn't create in invitation on someone's computer (written proof) to show you that has whatever you will okay on it

If you think they will lie anyway, why think they will only lie verbally?
Nope. The parent did her part--she provided written invites with all of the information. If a child is hurt it is not her fault that the child and that child's parents ha issues.
I will say i would require every kid to get me a parent's phone number before we left, in case of an emergency--but I would not be calling and speaking to the parents--just having a list handy.
I think it is entirely reasonable to assume that is the child is brought to the party you have given your permission for them to be there. If the party invite did not say they were leaving town you would have a right to be angry at the host parents, but if the invite said that--then no you have only a right to be angry at your child for not being truthful or at yourself for not finding out what the party is about.
Again--easy enough for the kids to print out an invite. Mine make up and print out their (legit) ones with no help from me

Anyway, yep I trust my kids. When the weather is nicer it is not at all uncommon that DD14 calls after school to say that a group of them are going walking downtown, taking the train to another town to visit the castle or botanical gardens, going mini golfing, etc. I assume she is telling the truth and am happy she is out and having fun with her friends--and I enjoy the bevy pf photos that crops up on facebook that night
I actually didn't lie to my mom. We are all different, and our kids are too. I am sure my kids WILL lie some, but hopefully not too much. Maybe they will feel less compelled to do so since they know they have a lot to lose (ie--my trust which they currently have). DS12 has a friend whose parents are fairly strict. This friend is always findin ways around the rules and his excitement is clearly not about doing the things themselves but about having put one over on teh parents (most recent case he figured out the PIN to the parental controls for internet and his DS. It is obvious from his reaction that he is not that interested in the sites he is visiting, but he like the thrill of knowing he should not be visiting them---of course I called his mom that night and let her know and that PIN will magically change in a few days; she is giving it time so he does not realize where the info came from--she loves that he hasn't figured out how sound travels in my house and lots and lots of good info is gleaned

). We have no parental controls and my son doesn't go to such sites because they are "boring"
I am glad you feel better now. It sounds to me like your DD has good friends who are polite (all RSVPd) and honest