You can post the original URL in the message body text and it will show....just like any other page. If it is on your local machine and not on a web box somewhere, then yes, you'll have to make it available.
Now, most ISPs offer you the ability to have a home page and you can upload the file to that location, then post that link in the message body text and people can answer it. There are also companies that offer free webspace for web pages. Remember GeoCities? It is now part of yahoo but you get my point. You should be able to sign up for a free yahoo web page and put the video up there, then post the link in the message body text on meso and you're done.
MSN, AOL, and other content services offer this service for a fee.
One other option is to backend a webserver out of your home...in other words, open up a port on your firewall and NAT the firewall port back to an apache box or whatever webserver you are running. Typically, most ISPs do not want you hosting web content on a subscriber connection so you will have to run a high port number - well, anything other than port 80 or the other TCP server ports - sendmail, nfs, ftp, POP/IMAP,etc.