It does say;
A large hole in the left hand wing root fairing was observed followed by discovery of penetration at the underside of the fuselage.
So are they saying an object has entered the wheel bay and caused the tyre to rupture rather than deflate via the plugs. Its not so far fetched that a small sharp nosewheel part could have somehow been flicked into the scenario. Concorde might have a few words to say about foreign objects being thrown into the worst case locations. As far as continuation, while the PIC has final say, I'm pretty sure some conversation with flight ops and engineering would have occurred and a joint decision made, with a monitor for anything abnormal caveat, not knowing there were holes, just a deflated tyre. No problem having services in case the flat wants to smolder or come off and cause further damage on landing, if its already not doing anything in flight its hardly going to start causing trouble at a later stage before gear extension.