Why did Harry Reid vote against DADT?

After reading Scott's AP story on the failure of the DADT amendment to the defense spending bill, something jumped out at me:

Senate Majority Leader Harry Reid, D-Nev., also voted against the measure as a procedural tactic. Under Senate rules, casting his vote with the majority of the Senate enables him to revive the bill at a later date.

Which signals to me he knew it was going to fail all along, unless he engaged in some "No, you vote first -- no, YOU vote first" and cast his vote once he realized the bill was doomed.

I wonder what Lady Gaga will say?

(Her latest tweet is directed toward John McCain, not Harry Reid)