I suspect the invitation had nothing to do with family values, family attachments, or consideration of William's safety at all. The offer was very likely a strategy to hopefully show that EVEN the former Kaiser is fleeing Hitler, the Germans, and his own family and HAD to accept the good graces of his former death-struggle enemy, the English. Rather than remaining neutral, had William made such a choice, it would have been a public relations coup that would have substantially garnered and strenghtened the already strong anti-German, war-ready British government and citizenry.
If such an offer had actually been made, I think the Brits were wishing and hoping would accept and then the Brits would have made a huge deal out of it. In fact, I would not be surprised if a lucrative deal was not presented to Wiliam for him to accept the assylum offer.
It would also have been a nice slap in the face to Wallis and Edward, which many would have loved to witness.
However, at that time, William was cheering on the successes of the Wehrmacht. The Netherlands surrendered on May 15 and a month later when France lost the war to Germany, William sent a congratulatory telegram to Hitler on the success. So, I don't think William was afraid for his safety nor, at that time, very willing to join the other side in spirit.