LRZ's post in Throwing to unoccupied base during steal attempt was marked as the answer
As many people do, you are overlooking the "for purposes of making a play" language. In OBR, the rule is 6.02(a)(4): it is a balk when the "pitcher, while touching his plate, throws, or feints a throw to an unoccupied base, except for the purpose of making a play...." The NFHS version is, I think, 6-2-4(b): it is a balk for "throwing or feinting to any unoccupied base when it is not an attempt to put out or drive back a runner...."
LRZ's post in Pick Off Attempt was marked as the answer
What you describe is not a balk and the pitcher does not have to disengage. The OBR rule is 6.02(a)(4):
The pitcher, while touching his plate, throws, or feints a throw to an unoccupied base, except for the purpose of making a play; Rule 6.02 (a)(4) Comment: When determining whether the pitcher throws or feints a throw to an unoccupied base for the purpose of making a play, the umpire should consider whether a runner on the previous base demonstrates or otherwise creates an impression of his intent to advance to such unoccupied base.
LRZ's post in 3rd strike run score... was marked as the answer
No. OBR 5.08(a): "One run shall be scored each time a runner legally advances to and touches first, second, third and home base before three men are put out to end the inning. EXCEPTION: A run is not scored if the runner advances to home base during a play in which the third out is made (1) by the batter-runner before he touches first base...."
This is not a time play.
LRZ's post in Scoring by tagging up on fly out was marked as the answer
ATLROSS, please note that "force" is a term of art which is not applicable to a runner returning to tag up after a catch, as the catch of the BR's fly ball removes the force. Here is how OBR defines the term: "A FORCE PLAY is a play in which a runner legally loses his right to occupy a base by reason of the batter becoming a runner."
OBR 5.08(b) has an approved ruling virtually identical to your query: "APPROVED RULING: One out, Jones on third, Smith on first, and Brown flies out to right field. Two outs. Jones tags up and scores after the catch. Smith attempted to return to first but the right fielder’s throw beat him to the base. Three outs. But Jones scored before the throw to catch Smith reached first base, hence Jones’ run counts. It was not a force play."
LRZ's post in Dropped 3rd strike was marked as the answer
Under OBR Rule 5.05(a)(2) Comment: "A batter who does not realize his situation on a third strike not caught, and who is not in the process of running to first base, shall be declared out once he leaves the dirt circle surrounding home plate."