I can only attest that it is common folklore that Hilbert is the last mathematician to have understood all of mathematics (I can't recall where I've read this; but I know I've seen or heard this in more than one place).
But this is folklore; I of course can't judge whether this is true (or, or if other mathematicians, you (you mention Picard, and Joel David Hamkins even says von Neumann) truly fit this criteria. I feel this is very subjective and the only people who may be allowed to make such claims should be experts very knowledgeable in the history of mathematics.
EDITED: Picard was born 6 years before Hilbert, and they both died in the early 40's. So chronologically it would make sense if they both represent the last generation that could have had a full understanding of all of mathematics.