I feel alone on an Island here... did I miss the intent of this question?
Did you want to know how the FHA is funded (exactly as you asked) or did you want the answer the agents gave you about how an FHA mortgage is funded?
FHA is an entirely self generated program. FHA does not utilize tax-payer funds to operate and is funded entirely from mortgage insurance premiums it collects. This is the reason FHA premiums are going up and in some cases, may never fall off. Some estimates have FHA short 13 billion dollars and they need to raise premiums to recoup that.