Rich, the guy in the video makes the things quite dramatic, perhaps because his rims are made of carbon fibre. With our aluminium alloy rims, it is not that problematic. There are two difficult moments with the tyre change:
1-After the wheel has been removed from the bike, you need to "break" the tyre bead from the rim. It is done by energetic squeezing both sides of the tyre with fingers while rotating the wheel. Once there is some space between the rim and the bead, it is easy to insert a tyre lever between the bead and rim, and the rest is simple.
2. It is far more difficult to insert the tyre bead onto the rim when replacing the tyre. There is no doubt: the inner surface of the tyre needs to be powdered with some talcum in advance, before putting a little inflated inner tube inside the tyre. Then, with one of the beads already placed onto the rim, the process of squeezing the other bead onto the rim (starting at the valve) begins. And the hard moment comes when the last part of the other bead (opposite to the valve) doesn't want to get in onto the rim! The answer? Use dish washing liquid (or soapy water) to lubricate the inner part of the problematic bead.
The guy in this otherwise excellent video has missed two important steps:
First of all, he didn't powder the inside of the tyre (it makes the interaction of the inner tube and the tyre better). Secondly, he didn't lubricate the second bead (he mentions that only near to the end of the video). Not lubricating the second bead on tyre replacement leads to frustration. (If the tyre lever is used for the last step of inserting the bead onto the rim, it is very easy to damage the inner tube). If the bead has been lubricated, it will jump onto the rim easily.
I hate replacing tyres. I had (painfully) to learn doing that.