What does OBJECT_GROUP actually mean?

I get the impression that then you call llGetObjectDetails with OBJECT_GROUP, you get the group that the owner had active at the time that the object was rezed. But I have had strange experiences where I changed my avatar’s active group and this caused llSetPos in existing objects to fail to work into areas that used to work. Is there any documentation to explain what llGetObjectDetails([OBJECT_GROUP]) is returning and what it actually means? Has anyone else figured this out so you can tell me?

It should be the same group you see in the edit window's general tab, and yeah, by default it's what the avatar had active but you can change it there in the editor.

There was a corner case where if land allowed owner scripts and group scripts, an object set to the "wrong" group would work as long as the owner (or owner-like group member) was in the sim. I thought that was closed up in 1.26. Is it back to doing that in 1.27?

In general, on group land, you want to set the group of the object to match the land group, so that your avatar's presence won't matter.