Hello my sweet, we meet again.
Perhaps you have all this already, but just in case you don't, here goes:
Regardless of what the IGI says, it would seem that the family you are researching was as follows:
(Whether any of this is fact or fiction I have no idea.)
Randolf Nye (born in Denmark)
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William Nye=Agnes Tregian
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Ralph Nye
Now, if you look at
http://www.rootschat.com/links/0ny/ and scroll down to INDEX [4433] (second family from the bottom) you will see some reference to the inheritance of William Nye. The reason that I mention this is that it is in Uckfield, Sussex
Then, if you look at
http://www.rootschat.com/links/0nz/ and scroll down to INDEX [4438] (near bottom of page) you will see some reference to father Randolf Nye holding land in Uckfield,
and [4433] is mentioned yet again.
Since these are supposed to be actual published documents, they suggest that Uckfield was a major part of the life of this family. If William's son Ralph was born in Uckfield (as is suggested here and there on the Internet), then perhaps the marriage of William was also in Uckfield, regardless of where he eventually died.
So, if you are looking for William's place of marriage, I guess that Sussex, rather than Hertfordshire is the place where you should be looking.
And 9 miles from Uckfield there is a place called Horsted. Horsted is also similar to the mystery "Horned". Of course, that may well mean absolutely nothing whatsoever.
Anyway, whether or not those published documents actually exist or not, it all gives you a bit more to work with, I suppose. Or more accurately, it gives you more to worry about. Alternatively, you can simply throw up your hands in despair and shriek quietly to yourself.
Whichever it is, I bid you farewell for now, my darling Swampy, until our next encounter,
UKgirl