yes, this is crazy every other phone i had would automatic lower the resolution and send it.
"Every other phone you've had" probably didn't video in HD!
First off all, how are your trying to send? Via MMS (text message) or Email? If it's email, you have a little room to play with, but 20MB is pretty standard attachment limit (even if your email provider allows more, the person you're sending to may not). With HD quality video, you'll hit that 20MB in just a few seconds.
HD video can create very large file sizes, and simply isn't meant to be transferred that way. It's not an S3 setting, no device will allow you send files of that size via email and definitely not MMS.
For email, I'd change the video resolution down to a much lower one and try that...
*IF* you want to send video via MMS, what you need to do is go into the camera app, switch to video mode, then pull up the options. Under "recording mode" change it to "Limit for MMS". This will force the video to take a smaller resolutions and smaller file size so it can fit within the limits of MMS. Using this setting will probably help if you're trying to send via email as well.