Having exactly same problem with IPhone 4S and my Ipad3. Has anyone found a solution. I originally tried to send a complaint. And this is where it takes me. Other people having the exact same problem. Has anyone got a fix for this, before I am, not only permantly refused Dr appointments from getting the wrong alerts or go just plain mad.
I too have been dealing with this issue and have updated to IOS 7.0.3.
I too set both alerts for every event, and they constantly reverse.
I found a short term fix but I agree this is really a bug in the IOS.
Go to the default alert times in Settings.
Settings>Mail, Contacts, Calendar.
Scroll down to Default Alert Times.
I set Events to NONE
I also set All Day Events to NONE.
The problem seems to be resolvd for now, but not sure why this had to be done.
I'm not sure if you've figure this out, but I was having the same issue. I'm using my Calendars with gmail, and I've realized it was a gmail setting overriding what I put in the Calendar app. I went and logged into my google calendars online and there were default setting there for alerts. Once I removed them, they no longer popped back up in my Apple Calendars.