Not surprisingly, turns out there was more to that speech that changes the context. Biden was lamenting Bush not involving the Senate in the appointment process and selecting too extreme a nominee.
“I believe that so long as the public continues to split its confidence between the branches, compromise is the responsible course both for the White House and for the Senate,” he said. “Therefore I stand by my position, Mr. President, if the President [George H.W. Bush] consults and cooperates with the Senate or moderates his selections absent consultation, then his nominees may enjoy my support as did Justices Kennedy and Souter.”
Considering Biden let the nomination go out of committee in the first place, pretty much kills using that as anything other than an out of context gotcha. It's still political weaseling, but the usual and expected sort. Big difference between "plz select a more moderate candidate" and "we're going to reject anyone." Especially given the timing difference.