UPDATED:
I figured out the following by playing with the numbers in the php.ini in /wp-admin:
The add upload page in the admin area seems to always display the lower value of either post_max_size and upload_max_filesize.
In my case, post_max_size was lower than upload_max_filesize which is the reason for “Maximum size of files for uploads” not displaying the 640MB but 64MB.
I suppose this has to do with this: see php.net docs as:
post_max_size integer
Sets max size of post data allowed. This setting also affects file upload. To upload large files, this value must be larger than upload_max_filesize. Generally speaking, memory_limit should be larger than post_max_size.