de Vere as Brother-in-Law of William I

The region of North Essex and Suffolk have a long heritage associated with the de Vere family. The question is why and how did they gain such influence.

It is generally reported in histories that de Vere was a companion of William the Conqueror and that he (a de Vere that is) either "came over" with William or that he was related to him and that he was granted land in England after Conquest.

What an A.I. search returned

When I queried whether a de Vere was a Brother-in-law of William I found the following:

It would appear from the AI response that the conclusion conflicts with the source that it quotes as a source - deverehouse.co.uk

I cannot find any other source that makes the claim that a de Vere was related to the Rollo lineage.