Alice: "Republicans would never support the Healthcare bill."
Bob: "Actually, I'm a Republican, and I support the Healthcare bill."
Alice: "Well, no TRUE Republican would support the Healthcare bill."
The No True Scotsman is an attempt to deny a group of people from a label, even though the label applies, because they disagree with something that the asserter believes to be a fundamental requirement.
Alice: "True Christians wear crosses."
Bob: "Actually, the Mormons don't wear crosses."
Alice: "Like I said, true Christians wear crosses. So Mormons obviously aren't true Christians."
I was watching TV with my mother, and there was a rapper on stage wearing a cross. She asked if he were a Christian, and I said, "I don't know. He's not a part of the Christian music scene, but that doesn't mean that he's not Christian." She was confused by my answer, because she didn't understand that what makes one a Christian is if they call themselves a Christian. You cannot invalidate my claim that I am a Christian by attacking my actions, or statements, because those don't matter. A Christian is a person who has belief in Jesus.
So, when people talk about RINOs, they're talking about people who are called Republicans, but obviously aren't true Republicans, because they fail to uphold some arbitrary condition that the asserter feels is necessary to call oneself a Republican. Even though, each of those RINOs has won the Republican nomination for their constituency. They are Republicans, and asserting that they're not true Republicans, by asserting that they are Republicans in name only, carries an implicit No True Scotsman argument right from the beginning. If they are Republicans In Name Only, then you're saying that a true republican would never hold their same positions. You are making an "ad hoc attempt to retain an unreasoned assertion" right from the start, because your unstated assertion is that a Republican would never hold the positions of the RINO. Although, since they are Republicans, you have to assert that they're not true Republicans, because they hold positions that no true Republican would hold.