It's theoretically possible, but would have terrible performance, be extraordinarily large and complex. Someone has written a USB interface for slow HID devices, quite slow.
The problem is that USB is quite complex with many layers. You can get chips that take over some of the lower level higher speed functionality (like the MAX3421E). Even with this, you'd still need a complex driver. For a USB Memory Stick, you'd also need a file system. There's a driver already written for the FAT16 file system for SD cards and it could be modified for use with a Memory Stick, but it can't handle FAT32 which is necessary for drives > 2GB. It also can't handle long file names or subdirectories.
There wont be a single answer to this, some of the cheap usb drives I have taken apart used an SPI interface that with some work you may be able to interface, I recommend you either A. stick with SD or B. take apart said usb and look up the components inside
"skipping usb"? You're on your own. I'm sure it's possible to do it, but it's not practical. Get a good dissecting microscope, a really fine soldering iron and a bunch of tiny tools.
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The problem is that USB is quite complex with many layers. You can get chips that take over some of the lower level higher speed functionality (like the MAX3421E). Even with this, you'd still need a complex driver. For a USB Memory Stick, you'd also need a file system. There's a driver already written for the FAT16 file system for SD cards and it could be modified for use with a Memory Stick, but it can't handle FAT32 which is necessary for drives > 2GB. It also can't handle long file names or subdirectories.
Any thoughts on skipping usb and directly interfacing with the memory from a usb drive?