The island could have been sinking. I have no idea.
This theory about the sun is just theory, also. When groups with a clear agenda tell me something is scientific, no matter their side, I remain skeptical.
A healthy dose of skepticism is always the way to approach any big claim.
However, unlike the popular with progressives greenhouse gas theory, solar activity leaves evidences of its effects that can be measured and studied. Also, telescopes were in use during the last big reduction in solar activity, the Maunder Minimun.
http://en.wikipedia.org/wiki/Maunder_Minimum
At that time and in cooler periods since, there are recorded accounts of these cooler periods coinciding with the reduction in sunspots.
As time went on, the mere visual notation that sunspots sometimes go missing became scientific measurements as to how that affects earth’s cilmate.
So, yeah, this may be “just a sun theory” but, unlike the wildly speculative greenhouse gas theory, it is one that is well understood and quite predictable.
It's difficult to prove that a scientific theory is true. You have to collect data FOREVER and the data has to agree with the predictions of the theory.
This contrasts sharply with the relative ease of proving that a scientific theory is FALSE. You only have to find one reliable fact which fails to conform to the theory.
So-called "Anthropogenic Global Warming" fails to predict the lack of warming experienced during the most recent decade. You may safely reject such a theory.