Not correct. You are right as to being a beneficiary of a foreign trust, as that is governed by IRC § 6048 and the reporting requirements there are much more involved, since you must report your creation of, interest in, transfers to, or distributions from a foreign trust regardless of amount.
But the rule for gifts received from a foreign person other than a trust is governed by IRC § 6039F, which does set a minimum amount for the gift to be reported to the IRS. The amount was originally $10,000, but the Code indexes that for inflation, which for 2019 is $16,388. Moreover, the IRS has increased the threshold for the filing of these reports to $100,000 when the gift is from a foreign individual or estate. See the Form 3520 instructions.
So while the reporting for trusts under §6048 and the reporting for gifts received from other than trusts under § 6039F are both reported on Form 3520, the reporting requirements are very different between the two. The instructions for Form 3520 lays all that out.