Kaneohe, the one rollover rule is measured irrespective of calendar year. The 12 months starts on the day the distribution rolled over (any part of it) was received and because it counts the received date, the last day of the 12 month waiting period to take another distribution to be rolled over is the date before the 1 year anniversary. Pub 590 A has an example where the first distribution is received on 1/1/2018. The last day of the waiting period would be 12/31/2018, so the first day the next distribution to be rolled over could be received would be 1/1/2019. The date of any of the rollover contributions is immaterial with respect to the one rollover limit, but NOT immaterial with respect to the 60 day deadline.
If someone messes up and receives a second distribution before the waiting period is up, there is some damage control in converting the second distribution. A conversion has 3 advantages over a taxable distribution – the 10% penalty is avoided, your total tax deferred IRA balance remains the same, and the Roth increase provides a higher quality IRA type than a TIRA. This is of course possible because a conversion does not count against the one rollover limit.