Given how far they were from the crash site, it seems very implausible that it was a rescue operation. The pilot would've had to walk 172 km in a single day to get to the location from crash site and other pilot. And the video of the jet getting shot down clearly shows they both ejected at the same time.

The two points on that Google Maps screenshot show the crash site of the downed F-15E in central Iran (lower black circle) and the location where the second crew member (weapons systems officer) was supposedly rescued by U.S. special forces (upper red pin near Shahrekord).

It might not have been an attempt to seize uranium, although given where they were that seems likely, but it clearly wasn't about the pilot. The reason why they'd make it up seems pretty simple. At first, they probably thought they'd use it as misdirection, and then when the whole thing ended up being a debacle, they tried to spin it as a successful rescue. If they managed to achieve whatever it is they were trying then they could tell a story of how they brilliantly tricked the Iranians.