When is BR Out?

[tibear]

UmpJM's post got me thinking(not always a good thing)

How is the following situation different from opening post: 1 Out, R1 and R3. Batter hits the ball to F4 who looks R3 back and then chases R1 back to first. R1 overruns first and is standing 2 feet in foul territory. F4 steps onto first thus forcing out BR (eliminating force on R1) then throws home as R3 is attempting to run home. R3 ends up save at home and original R1 steps back onto first. What's the call?

Is R1 allowed to run past his original base without being automatically called out or does he have to be tagged? Is this different then OP with BR retreating past 3rd base foul line?