The Syndicate’s first series has aired on ITV3 despite being a BBC One show. I think they even squeezed it into an hour slot, so must’ve done some edits to fit the breaks in too.
The Syndicate was an independent commission though, and after a certain period of time the rights for programmes made by independents (under PACT rules) reside solely with the production company who made it, not the BBC (*). That means they can sell it to whoever they want - though, to be fair, BBC Studios will sell repeats of BBC-owned shows too.
(*) This doesn't apply to shows previously made by the BBC (now BBC Studios) that the BBC has tendered to independents to produce (like Songs of Praise, Mastermind etc.) The right to those shows remain the BBC's, with the production company just being paid to produce the show.