The video is still posted at their original website,
http://howitshouldhaveended.com
I think the idea itself is an ancient one, in terms of the time LotR has been around; "Couldn't they just fly on an eagle and dispose of it that way." Which has no doubt been wracked by the rigors of Barrow-Downs debate in threads past.
The whole point of HISHE is usually either to point out weak flaws in the story or script. Obviously, the story would not have been NEARLY so memorable if it was so easy as to drop the ring - kerplunk! - in Orodruin. However, I think there are certain factors which may have facilitated this method...if things had come together differently.
Aragorn was able to distract Sauron by use of the Palantir. Since this was obtained from Saruman, he may not have had that available. But there is still a chance that, by mustering an army, they could have marched to Mordor under the same theory that the arrogance of doing so (with the un-depleted forces of Rohan and Gondor, mind you) would make Sauron think they had the Ring. (Was not Gandalf also able to strive with Sauron to distract him while Frodo was atop Amon Hen?)
These things don't account for Saruman and various other factors. There are all kinds of different ways that things could have happened. Fun to think about, but none would have painted the portraits of wisdom and courage and heroism that the series actually did. Nor would various side benefits have happened. Hobbits would have remained simple and unlearned to the outside world. Gandalf would not have become Gandalf the White. A balrog would still have lurked in the shadows of Khadzad-Dum. King Theoden would still have sat idle in his hall. Eowyn and Faramir would not have been joined...which was a partial result of Eowyn performing high and noble deeds, and yet not finding the satisfaction she sought. The dead under the mountain would not have found their peace. And so on and so forth.