Query: select groups by the latest updated item contained by them?

It's easy enough to select entities that I own ordered by time_updated DESC to get the latest.

What I want to do is instead select the groups that those entities are in. E.g. I create a blog post in group 123, then later a discussion post in group 234. I want to return [234, 123].

I've posted the $options array that doesn't do this (I can't tell what it's doing).

I think this could be done with a subquery to first pull the entities, but I'd rather not, and it seems like it shouldn't be necessary.

Any ideas?