Thanks for the link YLG.
My interpretation/understanding:
The surface temperature of the sun is only 5,800 kelvin which is the only thing we can be certain about.
From terrestrial experiments we know that the temp threshold for proton+proton fusion reaction (hydrogen+hydrogen = helium) is around 10,000,000 Kelvin to 16,000,000 Kelvin.
So, if the fusion model fails, we don't really know the temperature of suns "apparent" core. Considering the helium signatures we see in solar spectrum, it'd still be safe to assume that some kind of hydrogen fusion does happen inside sun. But we don't know at what rate(which is used to determine the age of sun). So we don't really know the age of sun, which is currently stated at 4.8 Billion years with roughly the same amount to go.
So, now! If age of sun is not known, we don't really know about the age of other stars as well. I just can't count the number of other threories that fail with the "fusion model of sun".
Seriously, how many of us say "I know what I am doing".
I am sure that most of them in the peer review board definitely says those words.