Not in the US, it's not. There have been many successful wrongful termination lawsuits bright about against companies that had no written policy in place. Not only for installing computer software but for just about any job-related activity you can imagine. Even if a policy is common knowledge and assumed to be understood by everyone, if it's not in writing, it doesn't exist as a legal reason for firing. Your country may have different laws but if the OP is in the US he has a good case.
I'm not surprised a law firm would think it could get away with such behavior, though. I once work