Honestly, it doesn't matter how much of the team he does own. I can tell you firsthand though that as the GP that he does in fact set the budget and did sit down with Tallon in the off season to identify which players we could sign and at what price point would be acceptable. So GP actually is more important than who owns the largest percentage of the team.
Not belittling the role of a GP.
On the other hand if the LPs are the majority owners, they will have a significant say so regarding the overall budget for player acquisition & retention - regardless of what it says in the articles of incorporation. The majority owners set the budget - the general partner's role is to decide how to spend it.
Viner is unlikely to go over budget without an okay from his partners. Even if he may want to spend the extra money, they may not.