I am afraid there is more than a little truth in this observation. But I would add a caveat: Their first loyalty is personal not to party. That means that it is to miss the mark to accuse the Bush/Rove faction as being RINOs or moderates or even country club republicans. Their loyalty is to the extended Bush family and its hold is very strong. It is animated in the President's case not by political philosophy or ideology but by his Christian faith.
Normally, this brings him down on the conservative side of issues, but not always. That is why he will spend $15B in Africa in a hopeless campaign against aids. He sees himself as a good Samaritan. Rove may countenence this ill advesed undertaking for political reasons but Bush is free of hypocracy. He is a true believer. That's why he could sign on to Kennedy's education boondoggle. It is a matter of Christian compassion. Ditto health care.
After he makes a judgment of right or wrong as a Christian, he extends and expects loyalty. Too often this is loyalty to a person like Putin or Fox or even Kennedy rather than to a principle.
Finally, and derivatively, he is a conservative.