Here's how I see it.
First and foremost we have all of the afforementioned connections to BP and Bledsoe. We all know how the percentage of a past BP player becoming a Cowboy is incresed 90% with this connection.
We have depth issues at WR. The problem isn't that we don't have anyone good (Hurd, Rector, etc.) but that we don't have anyone experienced. Copper is the most experienced player behind Crayton and he has what? 3 catches?
BP wants someone who can possibly play a role on this team, this year. Not another camp body or project. We need somewhat of an insurance policy in the event that (and it will happen) T.O and/or Glenn get injured. He won't be comfortable having his hand forced to depend on Hurd or the like before they are ready. Brown would provide a player, whom he knows and who knows the games well, that could play on last minute notice and be dependable.
Brown is also a versatile player capable of playing defense (though not likely) if necessary and can return kicks. He is also a team guy who is not going to gripe about playtime or practice, etc. Someone who could grasp the playbook quickly and easily unlike a newcomer to football. A one-year deal would suffice while the others bloom and learn from such an experienced vet.
Lastly, Brown, though old, is a much better player than 90% of the unknowns at WR that we will be likely to acquire in a measly trade for someone like Shanle. I'd just feel more comfortable with an accomplished and experienced, versatile team player who "knows the deal" as opposed to a young, wide-eyed, unproven guy in the event of an injured starter.
And if you think Brown is just a name and not a player than you haven't watched football the past decade. He's no Marvin Harrison... but he's no Peerless Price, either.