Look at the Senate Rules, Reid had to vote this way if he wanted to bring the motion back up.
I know this set of Senate rules (motion to reconsider, cloture) like the back of my hand. You are right, if he wanted to bring THIS cloture vote back up, he has to move to reconsider. But he could have let this cloture motion fail, let debate go on for some unspecified amount of time (2 minutes, 2 days, 2 weeks), then filed ANOTHER cloture motion, on the motion to proceed to the consideration of the very same bill.
Frist did this "multiple cloture motions on the same underlying vote" many times with judicial nominees; and the GOP had a series of 8 cloture motions entered and failed, plus 2 or 3 entered and withdrawn, ALL on a motion to proceed to the consideration of a bill to fund investigation into Whitewater.
A failed cloture motion does not kill the underlying bill, it leaves it open for more debate.