Answer

There are several different explanations of this among the medieval authorities (Rishonim). What I mainly remember is Rabbenu David on Pesachim, who brings several approaches on this. For example: a positive commandment overrides a prohibition only when the commandment is being fulfilled at the time of the transgression. The disqualification of a commandment fulfilled through a transgression applies only when the commandment comes to appease. A commandment fulfilled through a transgression applies only in cases of theft. And there are other such distinctions as well.