I don't think it makes sense either as Ohtani is essentially the only player in MLB who has a contract that pays for itself to the point where it's self sustaining and should have it's own separate budgetary allotment. Having said that I do believe there is some truth to this although I don't know what point this special budget runs out as there's no way it's unlimited in nature.
Change the wording from star player to impact player if that suits you better. I believe the likes of Pete Alonso and Alex Bregman likely fell under this "special" budget last offseason as the Blue Jays were reportedly in negotiations to add one of these guys as spring training approached. As mentioned by L54 Tucker is one of MLB's best/most consistent players year over year as he's ranked 11th in FWAR since becoming a full time regular in MLB in 2020, that's one of MLB's best players whether you think casuals know about him or not.