Why on earth would anyone need to use MYvariable in one place and myVariable somewhere else for the same variable? Sloppy habits should be actively discouraged.
I would agree with you if variables had to be declared before use, the fact they aren't means a typo like wrong capitalization would screw up your whole program and be very hard to track down.
Isn't there a way to have optional case sensitivity? If you choose not to have case sensitivity the compiler could convert everything to lower case when compiling. Or as Lee suggested you could have an auto-correct feature for lowercase UPPERCASE or Camelcase. Did anyone use TDK's IDE? That included a variable list which was very useful for avoiding typos. Will there be something like that in the AppGameKit IDE?
How about a third option, case-sensitivity with auto-correction. The main difference being if you have a variable called MyVar you CANNOT use a variable called myvar or any other capitalization. The editor would correct all instances of a variable name to the format of the first instance.
I really can't see the need for two variables with the same name, that is surely asking for trouble!