FFS Friday - Really?

There are times, many times, when I wonder if I'm the strange one and everyone else is normal. I think maybe this could be the case. The events of this week certainly have me wondering.
There's a lady I met at a class I took Chai to, she seemed nice and we'd chat during the class. Her son was really shy so I got Chai to make friends with him so he wouldn't be left out. 
One day we bumped into each other at the park and the boys had a great time playing together so we swapped numbers and agreed to arrange a play date. 
Not long after that she found me on Facebook. I have no idea how she found me because she didn't have my last name and I'm not visible in searches, but anyhow, it didn't worry me so I accepted her friend request. 
We arranged a play date for the boys but I had to cancel because I had gastro, so over the weekend I messaged her and said that Chai had been talking about her son Sam and saying he wanted to play with him. She messaged me back on Monday and asked if Sam could sleep over at our house so that she could have a date night with her husband. 
I thought that was really strange. She's seen me about six times, she doesn't know where I live and she really doesn't know anything about me. My instinct was to say no. My bad, I forgot to message her back (Facebook message not text message) and later Monday night after I'd gone to sleep I got a text message from her asking if Sam could sleep over. 
The next morning, before I'd had a chance to reply to her text message, I got a narky message from her saying "I can only conclude from your not replying that it's not okay to have Sam. Don't worry about it anymore it's all good, I'll try to find someone else or we'll just stay home." Really? WTF?
Seriously, is that normal? Would you normally Facebook message someone that you barely know and ask them to look after your child, then get angry when they don't respond quickly enough? 
I'm not up with sleep over etiquette as Chai has never had a sleepover, but wouldn't you call someone to ask them? And wouldn't you want to know them better and have been to their house a few times? What would it have been like for the poor child if I'd said yes and he'd got dumped at a strange house with people that he barely knows? For all she knows I could live in a share house with a whole pile of junkies!
Added to that, I know nothing about her son. Does he have food allergies, does he wear nappies at night, is he okay sleeping in his own bed/room, what does he eat for breakfast, is he lactose intolerant, what time does he go to bed, what time does he get up etc. 
Maybe I'm paranoid but there is no way I would let Chai go and stay at someone's house unless I knew them really well. In fact other than family members, there are only two friends I'd let Chai stay with, one is my best friend who I've known for 18 years and another is a very good friend who I spend a lot of time with and our boys are best friends. 
I also find it really odd that she got narky with me. How dare she? Why would she assume that I have any obligation to look after her son when she didn't even have the decency to call me? She knows that Tiger works away yet she didn't bother to ask if he was home, so clearly she thinks it's fine for me to look after her son when I'm solo parenting. Bizarre. 
I'm starting to think that I'm the strange one. Either way, I'm not going to change, I'm happy being strange.
End whinge.
Your turn.