I think Woody was afraid that Doug Marrone was going to just 'take the job' that wasn't offered to him, so he panicked and hired TB...
This micro-critical management scrutinizing is a getting a bit worn. There hasn't been a situation ever noted, that there is a certain NFL org rule that must be followed to ensure a successful franchise. Bottom line is, this team is in such disarray that, it goes way beyond who reports to whom or who has the last word in the matter. Who ever made the decision, whether one person or a committee of, the choice to keep a status quo on the QB situation is just plain stupid. It doesn't matter who answers to whom..... it's the decision making by whomever that need to be questioned.
Technically I think the Giants are the same way, or at least they seperate the HC and GM roles all the time and GM's don't generally hire HC's.