The famous 'full version' appears to be a modern invention — the short proverb is the original.
This is the internet's favourite missing half, and the evidence runs the other way. The proverb is very old: a version appears in the 12th-century German beast epic Reinhart Fuchs, and the Heidelberg manuscript line is usually rendered as kin-blood is not spoiled by water. It turns up in English across the centuries — in a 1652 sermon by William Jenkyn, in Allan Ramsay's Scots proverb collection of 1737, in John Moore's novel Zeluco (1789), and famously in Walter Scott's Guy Mannering (1815).
In every one of those appearances it means what people have always taken it to mean: family ties bind more tightly than other bonds. There is no known historical text containing the covenant-and-womb version. It is credited to a small number of modern writers — the author Albert Jack and the Messianic minister Richard Pustelniak are usually named — and it begins circulating widely only in the 1990s and 2000s.
So the correction that has spread across social media is itself the error. That is worth sitting with, because it shows the mechanism running in reverse: a claim that flatters a modern value — that chosen family outranks biological family — spread precisely because people wanted it to be true. The idea may be a good one. It is simply not what the proverb says, and no ancient source has ever been produced.