I absolutely do not believe this for one second. For starters, where are the actual numbers? Without these, how do we know how much of a difference budgets are making?
And I would be skeptical even with numbers, unless it were a deep dive that included differences in accounting methods. Here are some examples at PSU:
1. PSU budgets vehicles under Athletics, not under individual sports -- for wrestling, that impacts budget for recruiting and team transportation to certain events.
2. PSU's 9.9 scholarships are fully endowed. Management of all endowed funds (academic and athletic) is at the University level, so any mgmt costs are not budgeted to the individual sports. When the funds are granted to the athletes, are they transferred to Wrestling and then by Wrestling to the Bursar's Office? If so, then they might be under Wrestling budget. Otherwise -- if allocated to Athletics or directly to Bursar -- they would not.
3. NLWC resident athletes are technically University employees, though their salaries are IIRC paid by donor funds and managed outside the University system. However, they do receive University benefits (healthcare, reduced tuition, etc.) which are very likely not budgeted under Wrestling. (The same is likely also true for any NLWC staff if not also varsity staff.)
4. NLWC pays for varsity athletes' registration and travel for freestyle events -- Bill Farrell, team trials, U20s, U23s, Worlds, etc. This is not under Wrestling budget at PSU, but might be at other schools depending on their payment and budgeting methods.
5. Wrestling has to pay rent for BJC usage. This is an unlikely cost for other programs -- though some schools have wrestling-only facilities (Cornell, Ohio State) -- is facility maintenance under Wrestling or Athletics budget at those schools?
Etc. We can come up with many more potential differences without a complete deep dive into the numbers at each school.