Again the overall inherent advantage is in class size, but yet I don't hear you complaining about those lower half enrollment schools of some of the best classes. And why don't you have a problem with Lamar winning year after year? But Ill repeat my post.
The inherent biggest advantage to all is about numbers. Hence why they have different class's of football. One of the arguments on here was that private schools have such a big advantage because they can draw from a bigger area and population. Well the same can be said for a public vs public school. The argument is that private schools can pick and choose their better athletes who come into their school, which is laughable by the way. Well a bigger public school in that class has that advantage over the lower ones also. So no it isn't fair. And there will never be a true fair system for all.
Interesting fact here. Out of class 6, 5, and 4, and I pretty sure i have this right. Of the 26 out of 36 times a public schools made the state championship game since 2010, only 4 of them came from the lower half of enrollment number in that specific class.
If you add the 10 private schools who made it to the championship game out of those 36 teams, which they only won 2 of those 18 championships game, none of those private schools came from the lower half of the enrollment figures.
And no the multiplier wasn't suppose to purposely move up a school to another class. So to answer your original question, Yes a private school has the right to be playing any class that the multiplier has them in. Period.