I think, for it to be considered an "identified" flying object, they'd have to know more than just what country sent it — i.e. they'd have to know a class or designation for it and have an associated doctrine for dealing with it.
I remember a trend of people sending up weather balloons with GoPros a few years back. I would imagine having an F-22 come after it would make for a more exciting video than they normally get (although the "edge of space" footage is already pretty cool).
Or it's politically defensive. A lot of Republicans objected (properly? for political advantage? to encourage contributions?) objected to the way the previous balloon was handled. So this could be a more aggressive stance to avoid that again.
We shot down a Chinese spy balloon (confirmed) 8 days ago over the Atlantic ocean.
We then shot down an unknown flying object yesterday over Alaska.
Today we shot down another unknown flying object over Canada.
The government hasn't released any details about the objects shot down either yesterday or today.