I just looked it up and that's not true. Lots of IMGs take STEP3 after graduating to show programs that they can handle the curriculum/residency. It is just recommended that you take it during residency b/c most programs will pay for you to take it, so you can save money.
If you want me to post sources, I can.
I mean that's neat that they can do that. Are you sure about Americans who didn't complete PGY-1 and don't have a program's backing, which the OP seems to be?
I specifically recall needing my residency to sign off on a form before I could schedule Step 3. I'm glad that IMGs can get around it, I just recall needing it to get step 3 scheduled. They wouldn't fill the form out until July 1, which meant I had to hustle in order to get it in and schedule Step 3 for October of PGY-1 (got a week of light schedule for exam prep at the end of IM, took the test the first day and relaxed the rest of the week).
This was important because I started residency in 2019, so several of my peers who didn't get the ball rolling after starting residency ended up not being able to take Step 3 before the end of first year due to covid shutting down the testing locations and they continued to avoid scheduling Step 3 in PGY-2 on time either. The program gave them all extensions (6 months!) but ultimately four of eight of us took it too late (the one FMG had passed Step 3 before applying, the other three of us followed instructions). They got letters saying their contract wouldn't be renewed unless they passed by the fourth final extension date.
One passed and decided she was offended too much to continue to PGY-3 if a program was going to enforce its own policies and dropped out to go ruin some other program.
One failed and dropped out and has done nothing related to medicine or obtaining a license to this day.
One passed but then dropped out mid-way through PGY-3.
The fourth one passed and continued through the program.
This meant there was a gap in our year. A resident who had previously left the program after multiple step 3 failures was allowed to take her PGY-3 year with us. She had gone to a child fellowship for two years after having only done PGY-1 and 2 of psychiatry, then came back and graduated after PGY-3 with us, making hers a 2+2+1 = 5 instead of 3+2 = 5-year training for C&A.