Galliard (Zimmerman ed.) question

[Jeff Michael]

A student of mine is working on Galliard's sonata in G major. In measure three or four of the first (lento) movement, there's a dotted half note D tied to a sixteenth note on beat four. The balance of beat four consists of nine sixty-fourth notes beamed to said sixteenth note, all slurred onto one up bow.

Here's my question: are we to interpret the nine sixty-fourth notes as three triplets, each adding up to a sixteenth note's worth of time? And if so, shouldn't these sixty-fourth notes actually be thirty-second notes (triplets being three notes played over the rhythmic space of two of the written notes)?

Your wise insights would be most welcome.
Jeff