With the meaning that Feynman meant it was true then and now. From QED:

>The next reason that you might think you do not understand what I am telling you is, while I am describing to you how Nature works, you won't understand why Nature works that way. But you see, nobody understands that. I can't explain why Nature behaves in this peculiar way.

I think it's one of those famous quotes that was never said. The one I quoted was what he apparently said.

Quantum _mechanics_ cannot be understood, it is full of paradoxes. It contradicts classical EM and special relativity, among other things. A toy theory that was an important step to what came later.

Feynman's own QED is a part of QFT, but this is no longer quantum mechanics. Special relativity and quantum physics are reconciled since then. Now, we only need to reconcile GR and QFT, but this leap was so far beyond our attempts to scale it. Yet, QED/QFT/SM can be "understood" as there are fewer obvious paradoxes that plagued QM.