Bank of America no Cost Mortgage?

I was in my Bank of America branch yesterday setting up a new checking account. I noticed a sign in the lobby touting a no cost mortgage. I inquired with the personal banker about the details of the mortgage. He told me that they just raise the rate to cover the closing costs. I said to him that it doesn't sound like a no cost mortgage because there is a penalty in rate for the no closing cost option. I also said that if it were a true no cost mortgage then it should be the same rate as the full fee mortgage. He did not have any comment on that. My guess would be that there is no such thing as a no cost mortgage. Thanks BofA for confusing me.

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