I didn't watch the video, but if the key is encrypted (password protected) like it should be, what's the problem?

ssh key encryption isn't "lengthened" (it turns the password into the encryption key in the most obvious way possible). Unless your password is of the epic norse poem variety, it's crackable.

In the comments the author states that his private key is inside a TrueCrypt-folder, and that folder is on Dropbox.

I know that's reasonably secure but it feels terrible.