I think what the Nature paper author said regarding why AT3 might have less effect than hirudin is reasonable but not necessarily true.
You could also argue (I am not claiming to know anything extra here just speculating) that AT3 probably has a longer half life than hirudin and thus is around longer to do something in the circulation and via leaky junctions at sites of inflammation to get to where it has an anti-inflammatory effect.
I mean if you believe Kybersept subset-analysis than something does not jib here. I have only read the abstract though of the Nature paper study and this point may be addressed.