There is quite a difference between a newspaper owned by a wealthy trust (that doesn't have owners extracting profit from it) and one owned by a wealthy company (that has one or more people whose goal is to make as much money as possible).
Obviously that doesn't remove all biases, it doesn't remove all the ways people in the non-profit might still be motivated by agendas either related to wanting to be paid more by the non-profit or to make more money in their other business interests, and it of course doesn't mean they've done the impossible and become a perfect, infallible news organisation.
But it's still a hell of an improvement over the way nearly all other major newspapers are owned.