If I use this code...
...the API class doc says this format is 'mm-dd-yy', but no, it is some other format. Instead I must use this code...
What format exactly are you getting? And which writer?
The API class document simply specifies these constants and their values, that should match the relevant Excel format values; so the API document is not wrong.
What may be wrong is the code used to render Excel dates to readable dates using these values (for functions like toArray() or the Writers). I've not seen any evidence of this, but it is possible.
...which is a lot easier, and note CAPS are required or this won't work either...
All format codes should be case insensitive: capitalisation should be irrelevant. If this isn't the case, then there is a code fault... to identify this, I need to know exactly what method (Writer, toArray(), whatever) you are using to test this. Otherwise,
I need to test all possible permutations myself to try and identify the location of any fault, and (as I've indicated elsewhere) I have rather less time at the moment than I normally would have. Knowing what you actually get from PHPExcel_Style_NumberFormat::FORMAT_DATE_XLSX14
would also help. If you could provide a code example that demonstrates this problem, it would certainly help.