So, user_2 needs usage on the schema containing its newly owned reference table even though user_1 is performing the insert on a table in the other schema? Interesting. I though the validation was only dependent on user_1's ACL.
It was the only thing that made sense, given the error, though I agree it seems a bit odd.
I don't have time to experiment right now - but at a high level one would think user_2 would need usage and create on schema_1 in order to be the owner of an object in schema_1. There is no possible way for it to actually create its own object there without such permissions - that a superuser can do so leaves a possibility for a non-superuser dump/restore problem.
Whether the system allows you too or not I'd advise the owner of objects within a schema either own the schema too or have usage and create permission thereon.
