Might be a bit of each (dumping v overweight)
Dump, if on that 767 (it's not on all) is only from Centre Tank. Doubt emptying Centre Tank necessarily gets you below MLW.
My recollections (off the 767 for 18+ months now) for LH BA 767:
MTOW ~181T
MLW 136T
MZFW 126T
Wings take 36T?
So anywhere near MZFW (takes lots flowers back from EBB as cargo!) means only 10T of fuel for MLW. Still well worth dumping what you can, but it would take hours of droning around on 1 to burn off wing fuel - hardly desirable on 1 eng...
DD - presume the tyres burst sometime after stopping due heat? And not on the Landing Roll?
EBB was always interesting enough with 2 engines...
DD.. any idea "when" the engine actually failed? I reckon if you had one after V1, or shortly after VR, most of the pax would have noticed pretty early on with a low fly over Lake Victoria at low RoC. In that nobody noticed, maybe a more graudal failure a bit later on? Or IFSD after some indications etc...?