FACT CHECK TIME: Meghan and Harry's secret pre-marriage marriage

"... We called the Archbishop and we just said, look, this thing, this spectacle is for the world. But we want our union between us, so the vows that we have framed in our room are just the two of us in our backyard with the Archbishop of Canterbury and that was the piece that...

"Added Harry, "Yeah, just the three of us.""

https://www.townandcountrymag.com/society/tradition/a35757534/meghan-markle-prince-harry-secret-married-before-wedding/

Here is guidance on marriage under the law of England and Wales:

The marriage must take place in a registered building. Not all buildings are registered, so it is important to check first with your local authority. If the building is not registered then the marriage will not be legally recognised.

The ceremony itself can take any form, provided that:

1. it is in public
2. there are at least two witnesses present
3. either a registrar of the district in which the ceremony is taking place or an authorised person is present
4. both parties make the necessary declarations, for example, declaring that there are no lawful objections to the marriage

https://rightsofwomen.org.uk/get-information/family-law/marriage/#The%20marriage%20ceremony

I don't know whether the garden of a 'cottage on the grounds of Kensington Palace' is/was a registered building, but clearly the Archbishop of Canterbury is authorised to conduct marriages.

However:

(1) To be valid, a marriage has to be in public - i.e. the public must have access to the place where it is to be contracted; and

(2) There must be at least two witnesses to the marriage

As I've said in the madhouse that is Facebook:

Now let Meghan be interviewed by 

Judge Judy. Oh please, oh please!

There are exceptions - for example, where one or both of the contracting parties is very ill and cannot be moved; but even then two witnesses are required, even if the ceremony is carried out by the Archbishop of Canterbury.

Am I wrong? Put me right, somebody -  but not the newspapers who, right up to the Telegraph, have repeated this seeming bilge unquestioningly.