I agree... I too find it hard to believe the pilot couldn't notice a problem but then I don't fly the 767-300.
My only flat tire I experienced was on a business jet (HS125-800) where one of two tires on the MLG blew on landing because it was frozen.
We were at a light landing weight so very little power would normally be required for taxiing which was not the case and the aircraft was also listing to the side of the blown tire enough for us to notice it from the cockpit.
We taxied off the active runway and once with ground control asked the permission to have one of the pilots make an external visual inspection.
After the visual inspection we decided to taxi to the ramp which was about 500 feet away.
I can't even imagine taxiing with both tires flat and on the wheels/rims on the HS125 like the 767 did in this video.