Why can the post even be embedded at all in this case? If Gizmodo was forced to screenshot it to circumvent that you might have a point.
Yes it's public, anyone outside the group can find and see it, but it's clearly meant to be enjoyed by the people who made it or/and happened to come across it by chance.
This happens all the time though, and it's expected it might happen when you do it.
I live nearby a couple of lakes within a nice little forest, me and some friends found a spot a couple of summers ago a bit out from the trails which we improved to have a fire pit, some log benches, built a mobile sauna, and left notes that its intended to be used publicly. We knew that at some point it'd be found, and potentially ruined. It kinda happened, someone broke the sauna, we didn't feel we were owed anything since we decided to make it public, we knew the dangers.
If you don’t like this, then you can either try to restrict things to an extent e.g. by obscurity, like posting a YouTube video as unlisted, or building your fireplace somewhere public but remote or hidden, or you keep things enforceably private, like a private online group, or building on someone’s land.
A compromise would be to have screenshotted and crossed out names.
