I would ask the owners of that website, but by any credible research, except for the caveats I mentioned already, that would be completely incorrect.
There are many benefits to seaweed, but as with anything moderation is the key - even for things that have no downsides.
As for seaweed and thyroid cancer, this study concluded that:
“Further analyses did not indicate any association between seaweed intake and the risk of thyroid cancer on statistically adjusting for potential confounding variables as well as on stratification by menopausal status. The present study did not find an association between seaweed intake and thyroid cancer incidence in premenopausal or in postmenopausal women.”