True. The US Army has to cross the Pacific. But the point of the matter is that the Filipino troops were THE US Army. They were inducted in the US Army and were organized as the United States Armed Forces in the Far East or USAFFE. So the US Army had at least 70,000 troops already in the Philippines, aside from the regular US Army and US Marine formations.
What was needed were reinforcements and resupply.
Replacements could always be drawn from the native population.

Also, thanks for the comment. You gave me another idea for a what if.