I have looked at the source information Vance Mead has so helpfully provided. I agree with Vance that it would be good to see better source information to back up the current relationships shown on Wikitree. By Wikitree standards, the profiles of both William and Thomas are effectively unsourced. So if Charles Meads can provide more source information, that would be extremely helpful.
I also agree with Vance that we should never assume that long-held beliefs about lines of descent are necessarily right: we should always be open to new information. Even for people of much higher social status, long-held views of genealogists and historians about relationships can be overturned. That may be upsetting, and extremely inconvenient, but it does happen. End of mini-sermon.
Turning back to William and Thomas, the way I see things is this:
1. The 1619 Cambridgeshire Visitation shows a Thomas Mede moving from Somerset to Essex. Visitations are not always reliable. I find it difficult to reconcile the family relationships shown in the Visitations with what is on Wikitree. Heraldic evidence suggests the heralds were persuaded (I choose words carefully) there was a connection between Medes of the Clavering area and the Medes of Bristol and Somerset.
2. Isabel Meade married Maurice, Lord Berkeley in about 1465. She was daughter of Philip Meade of Wraxall, Somerset, a Bristol and London merchant and a Mayor of Bristol, who is described by Cokayne as of Wraxall, Somerset. There were all sorts of complications over lands, but Lord Berkeley held properties in various parts of England, including in Huntingdonshire, and at Great Chesterford, Essex if John Mead's 1977 article is right (and a very quick web search reveals other evidence for Great Chesterford being held by the Berkeleys around this time). Isabel is shown on Wikitree as cousin of the Thomas and William of this thread. John Mead used this marriage to support a connection between other Medes of Somerset and Essex, suggesting that the Berkeleys facilitated a move of some Medes to Essex. Other evidence aside, I do not find that an improbable scenario. But John Mead gives no sources, so it would seem to be slightly speculative.
3. About 50 years before the time of Thomas and William in the Clavering area, there are records of Medes there, but as far as I can see there is nothing to indicate their family relationships, which isn't surprising. (If I have missed something in Vance's information, I apologise.) This raises questions about the parentage shown on Wikitree, though I know from my one experience with some of my Ford(e) ancestors of Staffordshire, and from other research involving some surnames a bit rarer than Ford or Mede/Meade/Mead, that, even in rural areas, it can be dangerous to assume that people with the same surname living in the same area in the same century were necessarily of the same family.
To me as an I-hope-dispassionate outsider, none of this is conclusive one way or the other. It may be that the records just aren't there to say anything conclusive. But I don't think detaching people from parents is to be done lightly, and I would suggest that, unless further evidence emerges, the right course at this stage may be to retain the current parentage for Thomas and William, mark it as uncertain, and add some research notes. There is also scope for improving the profiles in other ways, adding sourced information, drawing on Vance's research. Of course if firmer evidence emerges, we should think again.
As I said, it would be good if Charles Meads could contribute any sourced information he has.
Although this is not a family I have researched, I would be willing to work with Charles Meads and Vance Mead on trying to improve the profiles of Thomas and William if they wish, using information they have. We could do this outside G2G. ... And I am sure there will be things to do on Thomas's children.