Obvous falsehood?
Only to the purposedly obstinate.
They came the same way, without pre-approval, they entered differently because approval was granted at the point of entry.
Read up on history.
You said that Irish immigrants came the same way as today's immigrants. You also said that their were no immigration laws to comply with when the Irish came. That is the history that you established for your point. But there are laws to comply with today so it is not the same no matter how obstinate you are about it.