But the tyres were supposedly being damaged by kerbs, not necessarily sliced (as evidenced by Vettel's, Alonso's and Rosberg's tyres being on the point of failing as they pitted), so immediate failures probably weren't guaranteed. Even if they were failing instantly, the kerb at Chapel has always been particularly nasty - I seem to remember someone losing a front wing or suspension on that kerb in the past few years.
Anderson was at turn 5 anyway, which for some reason the BBC kept on referring to as turn 4 throughout the broadcast. But in principle I think he's probably right - those kerbs are quite sharp on the inside edge and I can fully imagine a tyre spinning up would be damaged on the shoulder.
A mate on another forum pointed out another quirk. Hamilton's, Massa's and Vergne's punctures all came after the first lap with bits of carbon fibre liberally sprinkled across the track. After Gutierrez's failure (which may or may not have been connected, being the only front failure) destroyed his front wing and scattered debris all over the track, they deployed the safety car and went cleaning up the track. After that there were no other failures until cars started bashing into each other again. Perhaps it was just coincidence, but the timing does have some merit.
Ah, that's what confused me!
