All I know is that 51 Republicans couldn't agree to pass the McConnell bill and it went down to defeat. All I know is the final vote.
So,
Was McCain's afternoon "yes" vote on a motion to allow debate on the bill? Was the vote to allow debate a close vote? Was allowing debate the sole means to get to the final up-or-down vote on the bill itself?
If it was, then McCain voted "yes" so he could get to his "no" vote and make his pitch for a change in the current culture of the US Senate.
I used to follow the Colorado House of Representatives. The representatives there, of either major political party, often voted to allow floor debate (or second reading) on a bill, and then voted  upon the conclusion of floor debate to allow a final vote (third reading) just so they could get to that final definitive on-the-record vote -- and then would vote "no". That's common procedure.
I'm serious: If I am missing the point you were making, feel free to explain.