Not exactly correct. It's a little more complicated than that. If there's one transfer payment from a country on a list or lists of countries or companies under watch by the US Government, it gets reported regardless of how much the payment is.
If there's a transfer payment from a suspicious individual on the list to a person not on the list, it's reported. No matter what the amount.
Now as to your specific question, one payment or transfer from you to I that's $10k or over doesn't get reported. It's considered a one-off and not suspicious. I paid for one of my son's cars doing a transfer to the private party seller. It was well over $10k and no one asked me what it was even for.
If I'm making a routine (as in, there's a pattern) payment to an individual and deliberately keeping it just below $10k, it gets reported. Just as it would if there was a pattern of making a routine payment over $10k following the same pattern.
These transactions get a certain level of scrutiny to make sure they're legitimate and once concluded so, nothing happens. Nothing meaning neither party is even aware of it.
If there *is* an issue with the payments, both parties in the transactions would know about it as they'd be investigated and likely some form of legal charge would follow.
All of this because of AML (Anti Money Laundering) laws that are supposed to stop drug related transactions. At least that's what started it, the use of AML laws has been expanded far beyond that.