What a Japanese person wants to hear is sincerity. If you explain that you were mistaken on a matter of fact and unintentionally told him something that is not true, and you are apologizing, the vast majority of Japanese people will accept this in good grace. However, it would greatly assist your cause if you are, in addition to this, armed with the correct answer with the benefit of more research.

If you fulfill all those conditions, you have done everything you can. Just remember that Japanese people act polite because of social norms – not because they don’t get upset. If someone decides to pop off, he/ she will. Control that which is under control and let the world come to you. That’s more Zen than Japanese, but I still think it is good advice in general. – J