"Saberse" can be an intensified verb, but you would need to add something to make it explicitly something known by heart. Eg "Se lo sabe de memoria" = "He knows it off by heart" (or with other pronoun variations). "Conocerse" can be used similarly: "Me lo conozco de memoria" = "I know it off by heart." I can't guarantee this isn't an idiomatic usage though, as there are multiple uses of "conocerse" and it seems unlikely that some are not idiomatic.
For language mavens, well known and well-known each have a place: Well known is used when it comes after what it describes. Well-known comes before what it describes.
These sentences are both correct:<pre>
He is well known for his philanthropy. (Well known describes he.) His well-known philanthropy is the subject of a new book. (Well-known describes philanthropy.)</pre>
it should be well known not well-known.