I read the discussion to Counting the omer with doubt before the fixed calendar. A comment by user ID "Shmuel" says:
"Rav Soloveitchik said this is a very nice reason, but he disagreed with it. There is no real sefeika d’yoma today because we have a set calendar, but before Hillel the Elder established the calendar, there were years when people were unsure when Pesach began. Therefore, Rav Soloveitchik assumed that when necessary, it is very possible that people did count sefirah in this unusual manner."
I recall Ramba"m in Hilchot Kiddush Hahodesh discusses how long it took messengers to reach the farthest areas in Israel to notify people when Rosh Hodesh was. I think he said it took 10 or 12 days.
So, once people got that message, why couldn't they correct the counting after that point and just continue from that number?
For purposes of this answer, assume we followed Rav Soloveichik's analysis, here.