Erm, its definitely more than just Hashinshin saying that. I watch a lot of top lane streamers that are diamond+. Some of them are going mid and some just says that top lane is in a poor state right now. Top lane just has the least impact on the map during laning phase. Yes, I like to dominate my lane opponent, invade the enemy jungle, or gank mid. However, top lane is the lane that takes the longest to arrive and its far away from dragon. If you're using a champion like Darius, you can't just teleport botside because he uses ghost. Top has to sacrifice a lot more just to participate in dragon skirmishes. Since a lot of the game is played botside now, you might not get jungle help. And if you happen to get an enemy jungler that just constantly gank top for some reason, you can't really do anything. Honestly, I'm okay with that lol. As long as my jungler is helping with the rest of the map, then I'm fine. Let that enemy jungler waste his time at top. Might even sneak in a kill on the jungler. If you don't get people ganking top, its easy win. Top definitely has the easiest laning phase if its a pure 1v1. Its not as safe as mid, which means its easier to kill the opponent lol. You also tend to get jungler love with Rift Herald when you do really well. Other than that, its really just the matchups. If you're first pick, you can get counterpicked. Range top into melee top seems like an issue in high elo. They can still poke you under tower, so even tower hugging isn't safe.
After laning phase, it really depends how well your team did. Sometimes its better to split-push and other times its better to teamfight. If the teamfighting isn't going well, I rather just splitpush to put pressure and get attention on myself.
Either way, support isn't that hard to carry since a lot of people aren't really that great at support and you have a ton of map influence. Mid and jungle has a lot of map influence so if you're good at those roles, shouldn't be that bad to carry. Although, it definitely gets hard for jungle if the team isn't doing well. Laners don't typically help junglers that much either unless its for leash, dragon, or baron, so scuttler fights and invades might be difficult. Lack of vision on the map can also be kinda crappy when you're jungling since the enemy could possibly invade. People put way too much pressure on the jungler tbh. Adc is just...farming...support is the one doing all the damage and plays in lane phase. After that, you position well in team fights. If you know how to use player attack move to be a kiting god, you should be fine.
So which is the hardest role to carry? Idk, I guess it depends on your playstyle, if you have better micro or macro. But considering top lane does have the least map impact, I guess that is a valid reason to say that top is the hardest to carry. Bruiser items are also the most expensive items for absolutely no reason.