Ok, here's what I've tried to piece together so far. This is taken "assuming" that the story
https://www.dreamlandresort.com/forum/messages/18578.html is in fact trustworthy and correct, but this is juts a possible interpretation.
The MRF-24 was a test design done by Boeing leading up to the JSF program, due to its similarities with the X-32. This model has nothing to do with the YF-24 prototype.
The user in said forum claims to have worked on the YF-24 back in 1990, which means by that point, the F-22 and F-23 designations were taken up already by Northrop and Lockheed. This early 90s development period makes sense - the USSR collapsing would make a fifth-gen stealth fighter seem unimportant and not necessary, which is a decision that cut the F-22s production run short, resulting in <200 aircraft instead of the original 750.
The USAF wanted to replace the F-15C, that was the point of the ATF in the first place. With the potential of the ATF being cancelled, the USAF was scared they wouldn't get their F-15C replacement, and so contracted McDonnell Douglas to come up with a replacement that had comparable performance to the F-22/23, with the exclusion of stealth.
The user references seeing a picture of this YF-24, which was really an F-15 with backwards wings and strakes near the front of the intakes. While this image is fake, the user said it looked almost identical to the real thing. They were called out because they claimed they had an "untrained eye" and should know what the real thing looked like since they worked on it. However, the user most likely meant untrained in terms of what looks fake and what looks real, which wasn't too much of a common skill in 2006 when the post was created.
The YF-24 was most likely based off of the F-15, but because of its wings was too different to be called another variant. The user also states that the prototype was nicknamed "Eagle II", much like the F-15EX today. In 2006, the F-15EX was probably not even a concept yet, so that nickname could not have been here to create a fake story. Or it's just coincidence that the replacement for the F-15C today has the same nickname as it's potential replacement in the 1990s, and a random forum post in 2006.