No. Venture capital operating companies, hedge funds and private equity firms are allowed to hold minority shares of SBIR/STTR awardee so long as they do not have control of the awardee company and so long as their affiliation with the awardee, if any, does not put the awardee firm over the size limit. The exception to this is if the VC is itself more than 50% directly owned and controlled by one or more individuals who are citizens or permanent resident aliens of the United States. In such a case, that VC is allowed to have majority ownership and control of the awardee. In that case, the VC and the awardee, and all other affiliates, must have a total of 500 employees or less.
For SBIR awards only, some agencies may make a portion of their awards to companies that are majority-owned by venture capital operating companies, hedge funds, or private equity firms. This is allowed only if no one venture capital operating company, hedge fund, or private equity firm holds more than 50% for the stock.
A list of agencies can be viewed here.
If a VC owns a minority share of an awardee firm, and is found to be affiliated with the awardee firm, then the awardee is only affiliated with those portfolio firms that are majority owned by that VC or if that VC holds a majority of seats on the board of the portfolio firm.
For awards from agencies that have elected to allow small businesses that are majority owned by multiple VCs to receive awards, the VCs that own a majority of the awardee must have a place of business located in the United States and be created or organized in the United States, or under the law of the United States or of any State.