Corporations are viewed as collective nouns to be used with plural verbs, where as "group" is a collective noun that is treated as singular. I can't think of a context in which I'd use a plural verb with it, but I can think of dozens of such nouns that I would. You can say "The group is complying. They have an obligation." without it sounding awkward, however.

Something about formal, notional and situational agreement[0].

The "they" explanation just helped bridge the gap in my mind.

[0] https://en.wikipedia.org/wiki/Comparison_of_American_and_Bri...

You're overthinking it. If a group of people are complying, you say "they are complying". Your example is not a valid parallel.

I think you would say "the group are complying" when you want to specify that the group as individuals are complying (or when, like me, you don't grammar too well).