That makes sense, but unfortunately Riot is notorious for their lack of proper documentation. For instance, the EUW website doesn't even have Xayah and Rakan (let alone Kayn) in its champions list. Regarding damage type, the most clear case of conflict between Riot's classification and actual data is Aatrox. Riot says his damage type is mixed. However, I've checked three analytics websites, each with their own data, and they all agree that Aatrox deals on average about 85% physical damage and 12% magic damage. That's not mixed at all. These are the pages:
champion.gg/champion/Aatrox/Top?
leagueofgraphs.com/champions/stats/aatrox
lolalytics.com/champion/Aatrox
My wild guess is that at some point in the development of each champion they evaluate what damage type he's likely to deal mostly and they include that information in the client. After dozens of patches and countless changes some champions end up behaving very differently, but Riot doesn't update the information. I identified and updated in the wiki page about a dozen such cases.