Totally agree.It's actually a 90 day rule (rather than a 3 months rule).
Since there are 31 days in August and 31 Days in October, it looks like the earliest you can mail an N-400 is on August 16. However, it is a really good idea to tack on at least a couple of days, to avoid any conceivable counting problems which do happen. You really DO NOT want your application rejected because the IO decides that you submitted it one day too early, before becoming eligible. So I'd suggest mailing your application on Aug 18 or Aug 19.