Should Umpires correct unchallenged mistakes?

[NM FP Ump]

Okay, a little help here. Along the same line as the OP, but a little off topic, as usual.

Last weekend’s scrimmage game. R1 on 3rd, R 2 on 2nd, two outs. Ball hit to F6, she throws to 1st, F3 has to stretch to get the ball before BR gets to 1st. I give an emphatic, overhead out signal, and the 1st base coach is pointing at the base and yelling, “She pulled her foot!!” Strangely enough, that was all he said! He didn’t come up to me for anything else, and I didn’t avoid him (took my position on 1st base line extended to watch teams switch and warm up). Maybe he decided it was just a scrimmage game. So I asked my partner, “Did she pull her foot?” He says, “Yes, she did.” Okay, too late to reverse a call, but here is my question:

Should I have gone straight to my partner (PU) for a live ball appeal (in order to “get it right”) or should I wait for the coach to ask for help (i.e. check swing)?

Your opinions, please.