It took me a long time to actually come to a solution that works so I decided to write up on it. First I started by visiting the apple store and asking if I can buy anything in the store that will allow me to copy files from my phone into a USB stick. I didn't mind buying a gizmo to do it. They told me flat out this is not possible. However, I noticed apple had a tool called the Camera Kit, that allowed connecting USB to the phone. However then I was told this is for copying files from the camera to the phone, not the other way around.
I kept looking and finally saw another solution that required a jailbreak. However I am using iOS 7 with my iPhone 5, and it is not jailed break yet.
So I kept looking and finally found the solution and tested it fully.
here is what you need to do:
1. Buy a RavPower Device http://www.amazon.ca/RAVPower%C2%AE-Wireless-External-Streaming-RP-WD01/dp/B00AQUMZRA
2. use SD cards, or USB disk for storage. I got this for example:
http://www.walmart.ca/en/ip/western-digital-my-passport-1-tb-usb-30-portable-hard-drive/6000048930380?gclid=CJz28v-S9rsCFVLxOgodqiEATA
3. put the SD card or USB device in the RavPower
4. connect the RavPower to the phone via Wifi
5. done.
The application on the phone is called AirStor and it allows you to copy files from the phone to the USB or SD card, copy between SD and USB devices on the RavPower and even streaming from the RavPower to the iPhone or IPad.
I was not sure it is all going to work, so I tested it fully and it works great.
Overall price for this solution is about $150 (with the disk)
It is too bad the iPhone locks you this way, I guess it is a way to get you to buy the bigger storage phones. This problem however does not exist on most Android phones. The S3, S4 and G2 phones I have tested can all connect to USB storage or SD with no problems.