This type of story, a true test of the A2A ability of the F35 has been awaited for a long time, it's going to be a feeding frenzy, so I'm sure more info will come out regarding the source and possibly pilot who wrote it. Again, both these sites are very good at verifying their sources, and Tyler Rogoway has been doing this a long, long time, and probably has confirmed it before he would ever post it. He's actually a defender of the F35 as well, particularly the B.
Time will tell, but it would surprise me if this was just cooked up by some cook who dislikes the F35.
edit - that's actually a good point about the tanks and the imposed limit on Gs on the F16 with them. I'll ask that in the comments there, a lot of US pilots post and respond there.