He didn't say "open source doesn't solve problems", he said "open sourcing doesn't solve problems". The verb is very different to the noun.
Yes there are open source softwares that once completed are efficacious in solving the problems they were designed to solve. The point yeukhon was making was the act of open sourcing a project alone doesn't somehow inherently solve problems in its development. At least in this case not the two enumerated problems he sees with the healthcare.gov project.
Open source is a development model that encourages sharing and redistribution of source code. It is not a term that can be applied to the making public of government secrets, which has nothing to do with the encouragement of information sharing.
When Wikileaks gets their hands on government secrets and puts it on a website, they haven't made those secrets 'open source'. That word doesn't even make sense in that context.
Even if I get my hands on the source code of Windows and put it in a GitHub repository, I still haven't made Windows open source.
Yes there are open source softwares that once completed are efficacious in solving the problems they were designed to solve. The point yeukhon was making was the act of open sourcing a project alone doesn't somehow inherently solve problems in its development. At least in this case not the two enumerated problems he sees with the healthcare.gov project.