Fakenheath is a humorous takeoff of the name of a British airbase: RAF Lakenheath.
The aircraft featured in the episode are RAF Tornado fighter/bombers, not USAF F-16s. The former are twin engine aircraft, with signature beveled air intakes below the cockpit, where the latter are single engine, with smaller curved air intakes.
When Peter and Lyle go to the USAF base to find Brad Johnson, we see a sign at the main gate that reads 148th Fighter Wing, RAF Fakenheath. That's a clever play on the actual RAF Lakenheath in East Anglia, where the USAF's 48th Fighter Wing is based.