Bush... What Bush?

Scenario: Poulter's ball is in/behind a small bush on the 7th. TV tower is roughly half-way between him and the flag, about 80 yards away.

Rule: If the TV tower is in his line of play, he gets a free drop sideways, til he has a clear line.

Referee/Poulter Discussion
So Poulter wants to drop out of the bush, as he claims he is going to hack the ball through the bush towards the green. The Match Refree says that the ball can't go through the bush, so going toward the pin is not a "viable line of play". He says the only shot available is to the left of the bush, and the TV tower is not blocking that shot, so no free drop.
The Chief Referee is called, and asks if Poulter would hit the shot for the pin if the tower wasn't there. Poulter says yes, so a free drop is awarded.

Outcome
The free drop would be into a cactus, so Poulter opts not to take the drop, plays to th left, away from the thick of the bush, and still only moves the ball a short distance.

Right or Wrong?
Judging by the shot he actually hit, going through a light part of the bush to the left, there is no way he could have gotten any distance through the centre of the bush. So there's a case to be made that the TV tower wasn't in his line of play. That said, if there's a 1% chance the ball does have a way through, he's entitled to a drop.

The problem is, if he's denied a free drop, tries the shot and gets it far enough so it actually strikes the TV tower (proving it was a viable line of play), the referee will be in serious trouble. But it does seem there wasn't any chance of the ball going through. Note that taking the Match Referee's logic, if the tower had have been to the left, where he suggested Poulter's only viable line of play was, and not between him and the flag, he would have given a free drop on that basis.

It's a rare example of a need for a subjective view on the rules. You can't have an objective view of which lines of play are viable and which aren't. It's up to the referee to judge if the player has a chance of hitting a recovery shot, which is an odd situation to have, but is there any alternative way to have the rule? The chief's way of making it objective was basically to take the view that if the player says it's a viable option, it's a viable option. But this can't hold water when the bush is twice a big and thick, and it clearly isn't an option, but the player says it is.

What would a referee have done at Medinah in 1999 if there had have been a TV tower short/left of the green a player said "I know I'm behind a tree with 170 yards to go, and the TV tower is not between me and the flag, but I'm going to blast a 7 iron, missing the tree in front of me by a couple of inches, and slide it 60 yards left to right in the air, onto the green... but there's a TV tower in my way... can I have a free drop please?"