Touching Home Going Back?

[Manny A]

Brain cramp time: HS varsity game, bases loaded with one out. Batter hits a fly ball down the right field line. R1 assumes the ball is going to drop, so she heads home and touches the plate. However, F9 somehow manages to run the ball down and makes the catch.

By then, R1 is about ten feet beyond home heading for the first base dugout entrance. She hears everyone yelling for her to go back to third. So she does. She makes a beeline for third and beats the throw. However, she never came close to touching home on the return.

Or does she even have to? I honestly can't recall if the rule to touch bases in reverse applies to home as well, and I don't have my NFHS rule book handy to look it up.

Fortunately, the defense never made any sort of appeal.