But I think the usual corruption risks apply in either case. In the scenario you describe, it's not clear why a commercial sponsor would be motivated to do such a deal. The only direct rewards for the sponsor would be "ad space" in the department name and maybe some sort of reputational bonus for "funding science". But I don't see why a brand like Taco Bell would benefit from either one, especially if the needed investment is massive.
Also, even if there are no obvious conditions to the deal, this always risks inducing some degree of self-censorship on the side of the institution: Someone at the institution will think about what they can do to be attractive for more deals like this - and they'll probably be less welcoming for research that might drive away potential future sponsors.