Vault-Tec had access to vast knowledge of the government and other companies and probably tried to use all the technologies they could get access to. Having no option to manufacture or buy T-51b power armor in big amounts, they probably started their own research and produced something that was at least similar to the original.
The only one such known advanced power armor could be found in Secret Vault laboratories.
Other valuable armors like Metal and Tesla, that could be found in FO:BOS, might be produced by Vault-Tec as well during the same development project.