Good question L-38,
Be sure to read page one of that air safety article as well. It discusses a B-767 double engine failure.
Absent pressure from the boost pump in the wing tank, the engine should still be provided an adequate flow of fuel, via a gravity-assisted "suction feed" even if the boost pump is turned off, and even if the crossfeed valve is closed. At least, this is the prevailing conventional wisdom. The big question in this incident is why the engine did not continue to suction feed? The related questions include whether this is a fuel system design problem, and whether it relates to B767/engine combinations other than the Pratt and Whitney [UTX] engines on the United airplane (B767s operated by American Airlines [AMR1] are powered by General Electric [GE] engines).
After rotation, could a high deck angle of up to 18 degrees change gravity feed/suction capability of the fuel tank to the engine? I'll bet it's never been tried intentionally.
The 747-100 in the article doesn't say whether the engineer took off without pumps, only that they discovered it after flameout at FL200. He surely would have had some fuel panel configuration changes before then?
Before taking the runway I'd always make the S/O lean back and let me confirm no ambers on the fuel panel.....
Murphys law and all...