amateur recital can choose any BF?

Yes — Amateur Recital's ability reaches a unit at any battlefield, not just at Amateur Recital itself.

The text is "when you hold here, you may move a unit at a battlefield to its base." Only the trigger is tied to here (Amateur Recital); the target clause says "a unit at a battlefield" with no location restriction and no "you control" requirement, so any unit at any battlefield is fair game, including an opponent's unit. It gets moved to its controller's base, not yours.

Two limits worth knowing: you must still choose a legal unit, so something like Baron Nashor ("I can't be chosen by enemy spells and abilities") can't be picked (FAQ #10583), and if that move leaves you with no units at Amateur Recital you lose control of it in the following cleanup.