In a way.
Skillwise, yes, all players in a match should be of similar level, but that is not always the case, the Riven in my last ranked game said Taliyah and Rammus are ADC, complained how we don't have tanks while telling me I don't know how to build Taliyah because I have mage items.
[sg-zephyr]
She had no basic knowledge of how to move around the map, help or itemize.
Another example can be the Vi I had the previous game, if you check her game history, although she has over 120k mastery on Vi, she builds the same 3 items every game: Trinity, Black Cleaver and Hexdrinker/Maw. In my game, she went Hexdrinker against a 4 AD team with the support only had magic, the Lulu. She refused to gank, close to 15 mins in Lee had 12+ KP, Vi was still at 0. I was hard camped mid and my wards were of no help, Lee came from all the wildest positions you can imagine a Lee to come from, so if Vi didn't want to help me, I asked her to help the other lanes, she didn't want to.
This happened the other way around a lot, I've met a Nidalee who was good mechanically but failed hard on every other check box and since I was her enemy jungler, it was easy to shut her down, she started an invade at my red, so I conceded (4v3, not worth it), I stole all her red side jungle, my blue side and the 2 camps she left on red side, so she felt pressure to gank, and every time she got killed she felt even more forced to make stuff happen, she didn't knew what to actually do around the map.
TL:DR - Although the system sees the players in one match as equal skill, especially in lower elos, the skill disparity between players in that match can be super high. I've made a Tryndamere go 5 cs at 20 mins on top lane, I've seen 1.2 mil mastery Tryndamere feed hard (and checking match history after seeing that guy for the 3rd time in my games feeding on both sides, he wasn't talented at all).
While it's true that if you're good you will climb, the climb speed in lower elos is much slower than in higher elos assuming the player who wants to climb is of equal or similar skill as the rank he wants to climb from.