Had a similar experience last fall. A receiver was in motion in the backfield, and just a moment before the snap, turned up field, and was in the neutral zone just as the ball was snapped. (Pretty fast, but I caught it because it was on my end of the line) I blew the play dead, flagged it, and reported it as a false start. My white hat looked at me and said you don't have a false start, you have an illegal motion, and you let the play go. I said he was in the neutral zone when the ball was snapped. White hat went to the other wing, who could only confirm the forward motion, but not the neutral zone infraction. White hat looked at me again and said, that's illegal motion.

At halftime, we discussed this, and white hat was going off about me blowing the play dead. I was the only one in the room who insisted it had to be blown dead because the receiver was in the neutral zone at the snap, and his motion caused him to be there. So being the "least experienced" official, I "kowtowed" to the crew and said it would never happen again, but I expected them to do the explaining when a coach complains we got the call wrong. They said a coach won't complain. Lo and behold, we had it happen in the second half, and coach went ballastic because our enforcement changed. I explained to him that it wasn't a false start, but illegal motion and I made the mistake in the first half (but I felt like s**t saying that because I know I was right). He had a conference with the white hat, who said the same thing. Coach then asked me (after white hat went back to his position) what the crew threatened me with during halftime. I calmly said "nothing".

In retrospect, if I would have said encroachment instead of false start, I wonder if this whole scenario would have played out or not. But the point of the matter is, you see the play, you flag it, and then report it to the white hat. If there's any question, you will have a discussion, but ultimately the white hat shouldn't overrule you because YOU saw the part of the play you flagged.