First of all, you can not send a video, larger than 15mb via the iPhone. So if you are in less than 15mb it should go without issue. And try sending it over wifi, maybe you are using your 3g while having some 3g limitation? Well this never happens with me when sending video right from my phone.
Edit: And you are sending the video over mms??? Well it's logic that the video is stored on their website, i though you were sending it via email.