As from a discussion on IRC, I learned that RIOT currently does not support IP packet fragmentation/reassembly.

RFC4944 though seems to suggest not to have IP fragmentation/reassembly independent of the link layer fragmentation of 6LoWPAN, but to "collapse" that:

If an entire payload (e.g., IPv6) datagram fits within a single
802.15.4 frame, it is unfragmented and the LoWPAN encapsulation
should not contain a fragmentation header. If the datagram does not
fit within a single IEEE 802.15.4 frame, it SHALL be broken into link
fragments.

As it stands, the lack of that in RIOT makes it impossible to use a full UDP datagram payload (64k), but limits the latter to <1280 (the IPv6 required minimum MTU).