"2-12 ROOF COVERING must prevent entrance of moisture and provide
reasonable future utility, durability and economy of
maintenance. When reroofing is needed for a defective
roof, already consisting of three layers of shingles, all
old shingles must be removed prior to re-roofing."
If water is pooling in that flat area, it could be said that it may not provide "reasonable future utility" even if it's not currently leaking.
Also, this is from a FHA class I took:
"It's your job to make the call on the condition of the
roof. This is also true for flat roofs. HUD no longer requires a certification on a flat
roof unless the appraiser observes associated problems within the interior of the
dwelling (e.g., water stains on the ceiling)."