So your source is...nothing. Pure, unadulterated, unevidenced, rampant speculation. You say it was routine, and yet you don’t have a single, solitary example to back it up.
So you just made up out of thin air the claim that lots of foreign born kids got birth certificates saying they were born in Hawaii, without even so much as anecdotal evidence, do I have that right? And then you started repeating it as though it were a proven fact?
You made up a ‘fact’ based on no evidence whatsoever, and then started telling people it was true. How is that not, y’know, lying?
Your disproof is nothing other than an Ad hominum attack.
Which makes you less credible by far.
Suck it up buttercup.