Huh, how did I miss that...
Yeah, it sounds like technically only wins or losses is being tracked there (and which is what our rewarding data will be looking for), which is why that is the case.
If you know the only reason you missed getting a reward tier is because of a draw or two, you can probably send in a support ticket after claiming your reward when they become available and we can confirm if your total battles after draws would have counted. So long as too many people aren't doing that (or trying to abuse the system), there probably won't be a problem with giving you the difference if you fell just short.
In any case, thanks for pointing that out; I've passed that along to see if we can get a fix for the numbers displayed in that My Arena Stats popup.