I don't know how it will affect your chance of getting naturalization but I do know that if you lie on your application about anything then you have pretty much kissed your chances good bye.
If you lie about one thing & the immigration people find out, they will probably wonder if you are lying about other things. Best thing to do is to be up front about everything on your application.
If they need to talk with you about anything they will contact you & then you will have a chance to tell the whole story. In fact I believe on that application there is a place stating that you can explain situations in full detail.
I think if I were you, I'd find a different accountant, especially if your wondering if what he/she is telling you right or not.
With rules & regulations being really tight for everybody, best thing is to follow them right down to the very last letter.
Ellen