What facts is "countering" based on?

One,Counters DOES NOT mean you will lose if you play against one no matter what. You can go zed into Fizz and still win EASILY. It's not that , but also how you can outplay the champ, Teemo can only kite and poke . Darius can go heavy aggro and easily gank teemo pre 6 . At bronze-gold elo , You can win that match up with just straight up brute force. Your a darius main? More than another reason why you would win lane without even noticing. The reason why they say its a hard counter because its the strongest way to stomp darius ( By playing like teemo) now that DOESN'T mean you can't outplay your own counter pick . Then again , In high elo like d3-challanger , There are a few teemo mains that still get rekt by Darius all day . The way a teemo should beat a darius is easily is getting E first then Q . Never take w and Shroom across from darius and make him run into it. Of course with darius bleed + Ignite There's almost a high potential of killing .

How to Beat a Darius as teemo = In low elo people tend to just poke their way into winning lane while tanking minion aggro and missing cs. In exchange kill over farm. In high elo (trust me , im master tier and I've seen this almost all the time). They usually try to waste your flash as soon as possible by going stealth at level 4 and freeze lane infront of him . While doing so , at levle 6 , Plant shrroms infront of your minions and freeze there . CS Denied. Kill potential Denied. And a roaming Darius isn't that scary tbh so its k to be top all day .

How to beat a teemo as Darius = In low elo people just get dorans blade/Shield and just spin close to the target and drop him low as low as possible. In high elo , most of time , You'll see them get Long sword and 3 bots and rush a early brutulizer because of the CD , Most of them usually max at w before teemo hits 6 so he wont be able to move fast and kite you away.

It's all mental work. You know how to play a champ . Outplay him with just logic. The site I usually use is http://elohell.net/league-of-legends-champions/ Not all counters work , remember that.

The matchups just seem to go off votes, people upvote champions they think work well in that matchup and downvote ones they think do not. In this case Teemo has 23 thousand upvotes and 11 thousand downvotes while kayle has 7 thousand up and 2 thousand down.

Essentially it's an opinion poll asking thousands of players who has the advantage on the match up. It's very simplistic as it cannot take into account skill levels (for example some champions are very strong at higher ELO but not so much at lower ELO) and may take time to update after nerfs or buffs but it still gives you a rough idea of what people think of the matchup.

In Teemo vs Darius the problem Teemo has is that his auto-attacks are the same range as Darius's Apprehend. That makes it really hard to poke hard enough to take down Darius, especially once Darius gets to the point where a single catch chunks out most of Teemo's health or even kills him completely.

Teemo does have an early harass and poke advantage though, if he can maintain that lead he's fine.

It all relys on submissions and their votes (crowd sourced).

is it a reliable source?

well that depends: i always say "knowledge > skill > counter". I recommend playing LoL without visiting that site ever and ignore the chat in champ select that contains the word "counter".

My Opinion:

If you see X counters Y, this means X can punish Y easier for his mistakes. But a good Y player will reduce his mistakes to a minimum.

All the stuff on this site is a summarization of many peoples opinions and experiences and it's up to you if you believe them!