There is a convenient WP list of commercial jet airliners with numbers in service, though I believe this also includes cargo variants. It totals about 27,700 aircraft as of July 2020.
The US Bureau of Transport Statistics collect data from US airlines; one of the datasets they publish is Form 41 Financial Data, where "large air carriers" (revenues over \$20m) give general financial reports each year. Schedule B-43 lists an inventory of aircraft in those airlines. We can probably assume that not many airlines with under \$20m revenues operate a significant number of jet airliners.
A very quick and dirty count finds that as of 2020, US airlines reported 7117 operational aircraft, 4029 of which had a capacity of >100 seats and 5249 had >50 seats. All of these except 32x 70-seat Dash 8s seem to be jets, so let's take that as a cut-off for "jet airliners" - 5237 of them.
This suggests that US airlines have approximately 20% of the world's jet airliners, right at the higher end of your estimate. The number is probably variable by a few percent either way depending on how you account for cargo aircraft in the totals, but even a generous estimate here would suggest the US airlines do not go above about 25%.