So, reading between the lines some overzealous management type tried to give you some shit but HR found you had done nothing wrong therefore to protect the comoany and not make themselves look like the fools they are they decided to not give a penalty but put on your record they were right and you were wrong

Sounds quite typical of petty management to me.

Social media policy is stop employees doing things that bring the company into disrepute e.g. trashing your employer online, joining causes that could associate the company in bad company (like sites that encourage hatred), saying things that are illegal or could be construed as offensive ("I love Trump", for instance ).

I'm sorry you had to go through this, Poppy. I've been through silly pettiness like this where I didn't get on with a line manager. I can remember one visiting me trying to check I was actually off sick (it was day 2 after having no sickness in 2 years!) and he tried to say I wasn't in because I didn't answer the door. I said I was so why would I be answering the door to cold callers if I didn't feel like it. He then tried to confirm it was the right house by describing the front of my house. My answer was "that just proves you have driven past my house and not that you were even there on the day in question". We didn't get on and he was being petty. I got a warning.

They do this to feel in charge. You have the right to challenge the decision but they hope by not adding a penalty you let it slide.