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.