Purest speculation, but given that we know of Radagast that he "
became enamoured of the many beasts and birds that dwelt in Middle-earth, and forsook Elves and Men, and spent his days among wild creatures," it's entirely possible they only met while Beorn was a bear. I wouldn't go so far as to suggest Radagast didn't
know he was also human, but the reason they got on might be that the wizard thought of him as a beast first and foremost.
Even more speculative: the idea of an immortal hermit who cares for all animals is pretty common in fiction (
Medwyn of Prydain was my first thought, but I ran across another instance in, of all things, Terry Pratchett's
Carpet People recently), and I suspect it has mythic origins. Radagast would fit neatly into this category - the movies do so (hi Sebastian) - and so it would be plausible that Beorn was drawn to him after being injured in some way. Quite what could wound the Great Bear that badly, I'm not sure - though there were sorcerous powers at work in Dol Guldur...
...
Okay, no, I'm
not writing a story about Radagast healing Beorn of a Morgul-wound. I refuse.
hS