It is true that no documented link has yet been established between Joseph Ring (1646) and Thomas Ring (1700). Joseph Ring (1646) has been documented as part of the Marlborough, Wiltshire, England Rings who mostly migrated to Massachusetts and have left a large number of descendants in New England -- I call them the northern Rings. Joseph seems to have been the only one of that family who settled in the South, in Virginia. He had three sons, whom we know of, but two of them died as children and the third has disappeared from the record, with no known offspring. Joseph no doubt has many descendants through his female children, but they won't be called Rings.
It does seem likely that some researcher sometime in the past, frustrated with the absence of a documented link, just asserted that Thomas was a son of Joseph and left it at that. We cannot accept that assertion now, however. There may be a "missing link" between Joseph and Thomas, which may some day be discovered. But it seems just as likely that the southern Rings descend from an entirely different family. Doesn't the most recent DNA testing suggest an absence of close relationship between the northern and southern Rings? I believe that is the case.