Having raised 3 kids to adulthood (DS turned 18 in October! WOOT!!! FREEDOM!!...ahem, anyways...), I can say that yes, people are that clueless and invite themselves and their younger children to a party. I've always had a little extra for goody bags, and when I've had less bags than kids show, I would add extra goodies to the siblings bag and tell them it's for them and their siblings. It's not the other kids fault that their parent is a jerk; I would never want a kid to feel unwelcome or unhappy because of what the adults are doing.
One year, when DD#2 had her bday party (her bday is in July, so we had it at the beginning of June right after school let out, so her friends could be there before taking off for summer plans), she invited her whole class. She had just finished 1st grade, so she was turning 7. Everyone showed up, including one little girl with her younger siblings. She was told by her mom she could only go to DD's party if she brought her siblings (mom was not Mrs Beaver, if you understand what I'm saying). So, along came the girl, with her 4 younger sisters, one of whom was not potty trained and one of whom was not walking or talking yet. BTW, I had never met these people before, and had never even talked to them on the phone. No diaper bag or anything; and they walked to our house from theirs. They lived by the school, and to get to our apartment complex, you had to cross a big soccer field and a 4 lane road with no lights.

Now, I walked DD to and from school almost every day, so I knew the walk...and it was not one I would let my kids do on their own at those ages!
We were having the party at our apartment, so I didn't have to worry so much about paying for extra. DH was picking up Little Caesars (no delivery in our town from any pizza place, and it was either LC or Roundtable), so I had him get an extra pizza. Koolaid was easy to make more of; and I had plenty of veggies (carrots, celery, ranch etc) I had made cupcakes, so there were plenty; had mini cups of ice cream too, so glad I bought 2 bags that week! I just made goodie bags for the 2 older girls with all the extra stuff, and put suckers and sticker that I had laying around in bags for the non potty trained girl, but nothing for the baby, because, hey...baby. I walked the kids home after (because I am mom); the mom was home but only waved at me through the window when the kids RANG THE DOORBELL TO GET IN.
The NEXT DAY, they all show up at my house again. All of them. No diaper bag or anything...again. No contact with the parents...again. They didn't even know if we'd be home...they just showed up. Right before lunch. I fed them ramen noodles and carrot sticks (what I had enough of for 6 kids at that moment; DD#1 was with her other side grandmother, and no DS yet). DH came home from work and they were still there! I walked them home again, and asked the little girl to get her mom. Kid again rang the doorbell, she came to the door, and I told her I didn't mind her daughter coming to play, but I couldn't watch all her kids, nor could I feed them without notice, and that if her daughter wanted to come play, to please call me first, to make sure we are home and available. Mom was visibly hammered, and didn't even know where her kids had gone. She never called the police or anything to find them either.
They tried to come over again the next day, without notice and yes, all 5 of them, but we were leaving to go somewhere, and told them they had to go home. I walked them home, DH followed in the car to get me after I made sure they were safe. Never saw them again; the little girl wasn't in DD's school the next year (only 2 classes per grade, couldn't have missed her).
ETA: I have only ever been asked about guns once, and that was from the woman who was our then-new next door neighbor, who had a son the same age as DS. At the time, it was no, we didn't have any; same with a pool.