So far their publication on the contested point in discussion here is the press release submitted here. The field of linguistics has peer-reviewed journals like any other science, and it has authoritative secondary sources (surveys of world languages) and tertiary sources (encyclopedias of linguistics) and a large scholarly community of people who have more specialized knowledge than (apparently) any participant in this thread, including me, who know English, Old English, modern Scandinavian, Old Norse, and German well enough to dig into the data. What's more, historians have been publishing for generations on the general issue of how Britain was settled by the Angles, Saxons, and Jutes after written history had already begun in Britain, and how incursions by "Danes" in Britain were responded to by the local populations. This is not a new field.

A new comment, more recently submitted than your reply to my comment, puts the issue well:

Having studied linguistics I'd say the claim is sensationalist rather than sensational. English is a rather wild crossbreed of many European languages, all of which share the same Indo-European roots.

Old English is very closely related to Old Frisian and Low German. Later on English has been heavily influenced by Scandinavian, Romance (mainly French due the Norman invasion in 1066 - Norman French to be specific, which differed quite a bit from Île-de-France French at that time) and Gaelic languages to some extent.

That's very familiar to all of us who have formally studied linguistics of English. What's also dismaying familiar to anyone who has studied linguistics is the attempt of nationalists who are partisans of one language or another to claim a connection between their language and some language that enjoys great prestige (here, English). I have nothing against Norwegian. I speak it (a little), and Norwegian was my late grandmother's native language. I have nothing against German. I speak it (rather more than I speak Norwegian), and it was the native language and sole language of schooling for two of my grandparents. I also acknowledge, as I did in my original comment, that BOTH the North Germanic and West Germanic branches of Germanic languages influenced English. My uncontroversial and non-extraordinary claim here, agreed to by most linguists, is simply that the weight of influence on English is such, and the history of English is such, that English is better characterized as a West Germanic language than as a North Germanic language. The most frequently occurring word in English, which is "the," is one demonstration of that. The word "the" is a West Germanic word.

Historically, German, French and Latin have all been high-prestige languages, and scholars have focused on their relationship to English. There's been plenty of relation to find, no doubt! No one argues for direct lineage w/ Latin, but German roots have always been plausible and palatable.

Norse, though? Some would have found that scandalous. Borrowings--sure, ok. "Influence", of course. But lineage? No, certainly not.

This certainly gives a lot of fuel and authority to back people up to think they know what they're talking about. The truth is, nobody has a damn clue of how everything really went and trying to impress otherwise all degenerates to mere academic speculation.

The only thing of value such a field of study can produce is to connect a single observation or sets of observations that can be refined to something that's pragmatic and useful in actual world where life happens. If the researcher in the article were to be wrong by all academic angles but if what he thinks he has found turns out to have significance in how the English could learn Norwegian more easily or vice versa or how some similarities between English and some other language could be explained with that, then that's something constitutes undisputed value no matter what. If not, it simply doesn't, and any number of generations of academic prestige still doesn't make any difference.

People in science are often so confused about the importance of what's right and wrong, true and false while all they have is theories, and whereas they seem to be far better off whenever they simply follow the if-it-works-then-it-is principle.

If recitation of conventional wisdom as fact were the response to any new theory, we'd know everything is today exactly what we knew to be fact 500 years ago.

That the Earth does not revolve around the sun "is very familiar to all of us who have formally studied the cosmos" -- once upon a time.