If this were true there would be obvious connections, but there are none. That's the problem. Tolkien apparently refrained from making the Rohirrim into Anglo-Saxons. Instead, he devised a very generic culture for them which is equally applicable to many other Germanic peoples: Franks, Vikings, Goths, Vandals, Lombards, et. al.

: ... a people Tolkien spent his life studying,...

Tolkien spent his life studying language, and he studied many of them: Latin, Greek, Hebrew, Gothic -- not just Old English. He often spoke of his love of and influences from these other languages. He would not have been asked to help with the Jerusalem Bible had he really only invested his research in the Anglo-Saxons. His first love was language, and he happened to apply for and get a position at a university teaching Anglo-Saxon, but he did not abandon his interest in other languages.

: ... who he loved and appreciated and regretted that they were
: fading from modern awareness. Taking that view, however, we
: should note that Tolkien is not so simplistic, that he has
: mixed elements drawn from many peoples of the northern world.
: The goths are most often mentioned as a secondary element. The
: Rohirrim are thus largely modeled on (an idealized, literary
: model of) the Anglo-saxons, they are not the Anglo-Saxons.

[snip]

The notion that Tolkien thought only of Anglo-Saxons may be romantic but it is misguided and much too simplistic. And the notion that the Rohirrim are modelled on the Anglo-Saxons is simply not supportable. No one has yet been able to demonstrate any substantial connection between the two peoples, except for Tolkien's use of Old English to represent the translated language of Rohan, and that is no connection at all.

Tolkien was quite clear about not confusing the Rohirrim with Anglo-Saxons. That should have been sufficient, but apparently was not.
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