The Principal Investigator (PI) in an SBIR proposal must be primarily employed by the company submitting the proposal. That means they must spend at least 50% of their time working on the startup. This means the PI cannot be a full time faculty member at an academic institution, or a full time employee of another company.
This is what the SBIR.GOV site says about the Principal Investigator and the proposing firm:
"For SBIR, the primary employment of the principal investigator must be with the small business, and the proposing firm must perform at least 2/3rds of the R&D work in Phase I and at least 1/2 in Phase II".