Many federal contracts require small business to be part of the contract. So yes BORK wouldn't be the prime contractor, but they could be part of a subcontracting team. Or they could just have a supply contract with another company, who has the GSA/awarded-contract with the US agency.
Nobody is hinting or speculating that BI will do business directly with the USG. Bonding and other things required by FARs are a direct responsibility of the prime contractor!