Your classmates are wrong. ERAS opens for programs on Oct 21. We get all apps submitted prior to 10/21 on 10/21, and they will all be labeled "applied on 10/21". Applying earlier is of no benefit, other than it's done and you don't have to worry about it any more (which is a benefit). ERAS doesn't close to students on 10/21 -- you can still apply, add documents, etc.
Although it doesn't matter when you apply, I do recommend not cutting it too close to the deadline. Every year someone posts how their internet connection died, they were unable to submit on 9/15 (the usual program open date), they submitted on 9/16, and now they are convinced their chances are ruined. It won't matter, but they will still worry. So submit sometime before 10/15 just to be sure, then check on 10/21 to ensure that you have all of your documents assigned correctly.