Perhaps, though to be fair, much of this can be worked around (for how much? Tons o cash, eh?)
It's fairly standard that smaller/slower aircraft are very often more agile than the bigger boys - you just have to find the aircraft's strengths and play to those. For instance, the tiny T-35/F5 can commonly out-maneuver an F-15... at lower altitudes. At higher altitudes, the F-15 handles itself better in the thinner air of the upper stratosphere.
The F-16 is more than agile in lower altitudes, because it was built to be a combination air/air air/ground fighter, which leads me to believe that maybe these dogfights were conducted at lower altitudes... I am also curious (haven't looked) as to what the flight/fight profile of the F-35 is in the first place. if it's Air Superiority, then that usually means higher altitudes where there may be a better advantage. Anything else appears to be a whole lot of incompetence in design.
All that said, they had to know there were going to be compromises when doing the whole stealth (maneuverability) and STOL/VTOL (engine power) thing.
Or, best bet may be to scrap the damn thing and hold a competition for an aircraft that's worth a damn, and this time make the entrants build a working prototype *first*, without any governmental money up front... like they did in the old days.