Balk?

[Gre144]

Here is my problem. A pitcher who is in the set position while on the mound can do the following:

1) Step towards first while throwing the ball to F3 with R1 on first
2) Can step towards second while R1 advancing towards second
3) Can step towards third while R2 is advancing towards thirds

Logic tells us that he should be able to step towards home while R3 is advancing towards home without disengaging.

Where in Fed rules does it say that he must disengage from the rubber to put out a runner? To the contrary 6-1-3 says that a pitcher may turn on his pivot foot or lift it in a jump turn to step with the non-pivot foot toward a base while throwing or feinting as outlined in 6-2-4 and 2-28-5

6-2-4b implies that a pitcher may step towards a base with his non-pivot foot to retire a runner. There is no mention anywhere about the need for a pitcher to disengage inorder to retire a runner.
Thanks

Greg