It's as Kwaggy and Kyoto says on all parts. Outside of ranked and the grand majority of draft mode games (it's like ranked only without Elo attached to it), you'll see deviations from how it's shown in the video and their examples. But otherwise there is little chance of change. Riot has worked to try and fix, or alter some of these so-called "problems," but they're far from perfect.
There are team comps, and strategies which have shown to work, albeit sometimes called "troll." But when it does work, it can shake the meta,
hard.
As per the lanes, it's usually 1~2 top and bot, and always 1 mid, with a jungler. Usually the AP/caster champ is placed in mid, with the AD/range physical carry being baby sat on either top or bottom. Reason why it's the bottom is because of how easy the dragon objective is to take with ~4 players (mid, jungler, carry, and support), rather than 3 (mid, jungle, solo).
The AP is placed in mid because they scale the best with levels, and thus get their own lane to farm in.
ADs scale best with items, but are often fragile in one way or another and lack sufficient sustain, thus the support comes in, be it tank, displacement, or heals.
Most junglers are placed in that realm due to how well they do or don't scale off of items, power of ganks, and speed.
Finally, the solo lane is placed alone for the same reason as mid, but usually has some kind of off-tankiness to it, long sustain, and/or to supplement the mid. See the Vlad/Karthus combo from the video. They could have gotten, were they to have sufficient farm, an item called Will of the Ancients, its aura gives AP and spellvamp (sustain for casters), and with two separate champs having it, its effects are essentially doubled.
A while ago there was a some-what of break from this meta where the AD carry would be left alone and the support would literally roam the map to help other lanes get kills. The support wouldn't suffer from item loss since they were already expected to get 0 creep score to begin with, and the chosen champion's abilities were powerful enough that if they lagged by a few levels it wouldn't hurt later game. There was
some minor emergence of this a while back, but it seems to all but have died down from what I could see.
And hey, no worries. We're all loving and tolerable people! Ask the questions, and we're happy to answer! Everyone has their likes and dislikes, as well as allowed to play favorites. As long as they're open to conversation, s'all good my friend!
Besides, we wouldn't be here were it not for DotA's success...