This makes Paul a RINO ~ a Republican In Name Only. He does that to run for office. This is an old tradition in the Souf' and Texas. Run as a Republican to bypass the demands of the Democrats, or Libertarians or whatevers.
For many years the Republican party throughout the Souf' was a SHELL. Now it's not, so this sort of behavior is far more serious.
So, let's count up how many RINOs the Republicans have using different definitions
(1) Traditional ~ (as describe above) ~ that'd give us Perry and Paul.
(2) More modern ~ ustabe a Democrat, Libertarian or some other party but didn't run as one ~ that'd give us Michelle Bachman and that Johnson guy (although Johnson tried to run as a Libertarian the other day).
(3) Ustabe a Republican but joined or allied with Democrats ~ that'd be Jon Huntsman.
This leaves Newt Gingrich, Romney and Santorum as the only real, full scale, authentic Republicans running in this primary for President.
So, 8 candidates and 5 of them arguably RINOs under very narrow interpretations of the term.
Some still want to label Romney for his mind-numbed, robot-like, knee-jerk Leftwingtard government program outlook ~ but I think we already have sufficient terms concerning such folks so there's no sense wasting a perfectly usable term like "RINO" on them.
Only Gingrich and Santorum are clear cut, down the line, traditional Republicans.
I like your criteria for who’s a RINO and who’s not. I do.
That’s why I happily voted for both Bushes and against Regan.
/sarc