There are different flavors of SR-71
There's the SR-71, A-11, A-12 and the YF-12. I've seen honest-to-god SR-71s upclose and fiddled with their leading edges (it's a weakness with aeronautical engineers). You might have seen something different in the museum. It's also possible the titanium was stripped off. To me, a dead SR-71 in a museum is like seeing an American bald eagle with a cue stick rammed up its hind end (not a pretty sight). I wish they were still flying.
Gary