The NHL does not own the Stanley Cup.
They just act like they do.
When Lord Stanley donated the original Cup in 1892 to promote hockey in Canada, he passed control of the trophy to two trustees. The trustees took care of the Cup and created rules as to how and to whom the Cup could be awarded. The first Cup winner was an amateur team, Montreal AC, in 1893. It was not awarded as an NHL-only championship trophy until 1927, although it was won before then by NHL teams playing against other leagues’ teams.