When people say "Jungle can't carry" What they more clearly mean is that the role is the most heavily influenced by the instability of the game.
An excellent example, is a pretty simple matchup like Lee Sin vs Xin Zhao. I play the Xin side in a recent game, and heres how things went:
1.) Red buff, starting bot side, lane gank botlane, get both of lucian sums, and Lux flash, only used my ADC mf's heal. Raka loses no health.
(Lucian is forced to back, and MF is level 3 by the time Lucian gets the wave off his tower)
2.) I immediately run into and take the enemy blue side jungle, the buff isn't there, so I know Lee is top and probably going from red to toplane. I ping top that lee is coming, Riven dies anyway.
3.) I clear Lee's gromp and Wolves, flash on Diana mid, and kill her with Ekko, she loses her flash too.
4.) I take the other scuttle while lee is on his raptors, and Lee runs botttom to his blue side. I see him leaving on the ward at his raptor pit.
5.) My blue is gone, I take my gromp and wolves am oom, and ping my botlane that lee is coming because his bot camps aren't up. I even type it out "He's bottom and has no camps, he will be looking for gank"
6.) Clear my raptors, and then walk to golems. Botlane is pushed way too far up, and dies to the lee gank I ust told them was coming, I have on mana to counter with.
7.) My red is back up and I take it and back with over 2k in my pocket. Buy challenging, caufields, and boots.
To recap, I am 20 CS above Lee SIn at level 5, he is only level 4. I have gotten all summs out of botlane, except lux flash, my botlane has their summoners except heal. I have killed midlane, and my ekko is a level and 15 CS up. I perfectly tracked the jungler, pinged him, caught him on vision several times, and types to my team whats happening. They died to the ganks anyway.
I outpathed the lee, out ganked the lee, made better plays, against an opponent who was playing honestly smarter than my team, my Lanes are further ahead, and I am also winning the solo matchup in Gold and Experience.
Nonetheless, my opponent has more kills than me, but I have the shutdown.
8.) I gank mid again, take my wolves, gromp, and enemy raptors, while Diana is forced out of lane due to gank. Fed ekko and I go top to gank a Jayce, as riven crashes a big wave into his tower. We catch lee on golems, chunk him out, and then turn to dive the helpless Jayce. I micro perfectly, use my R to interupt his jump, slow him, hit every spell. Ekko is low from previous fight so its all up to riven, she spaghettis it, misses everytihng, and almost dies to turret forcing her to back meaning we get nothing for our troubles.
9.) My blue is up, so I go raptors, then to it, secure the thrid of three scuttles, then ping the riven to join me on Herald. Riven hesitates, is first timing riven in ranked, and doesn't listen to the call. Lee wastes his smite, and now all riven has to do is hit the eye on more time so we can secure the herald, I can smite for health, and we can get out with my ulti.
10.) Riven flashes into them both, misses her ult, kills herself, leaves me 2v1, then blames me after I barely manage to get the herald and die.
The call was fine, if she'd just listened it was easy herald, maybe one of us dies. MAYBE. Keep in mind, that at this time, I am significantly ahead of lee, and have my buff, meaning we win can easily get away without them pulling off something nutty or super risky.
Meanwhile, Mf is losing lane bottom, despite being spoon fed the lane levels 1 and 3 with the ganks, and keeping the lee sin far away form her lane. She singlehadedly is just losing as MF vs Lucian. Naturally she decided to go full lethality into a team of melee champs and lucian, who all itemize armor very well, and Lee sin, who gets it from his abilities. Genius.
11.) Some skirmishes occur, bad plays on both sides, I trade my life several times for plays not all of which work out, and despite this manage to remain far ahead of Lee and my own MF in both CS and xp. Its past 15 minutes and theres literally nothing I can do as a melee champ except chunk out most of their team and hope mine cleans up.
12.) I catch their lux, flash ulti their entire team into Ekko, who promptly kills everyone. Its a 4 for 1, our Ekko dies.
13.) I call baron at 22 minutes, with 4 enemy members dead for 30 seconds. Riven runs to the mid wave to celar it, and push to tower, while soraka backs and MF runs around doing nothing. I start the baron, and MF is the only one there, and raka still is coming from base. MF does no damage at all, and its not looking good, but ekko isn't here and we can't win the teamfight with no resist and half health.
14.) Ekko says he can zone them out, and manages to do so quite well. Riven, instead of helping finish the baron before lee respawns and arrives, runs off to do nothing because she has no summoners or ulti, and the enemy team is lux jayce lucian diana, al of whom will booty balst her if she tries to go in solo.
15.) MF still does no dmage to baron, and we almost get it, only to have it stolen by Lee whos smite combo exceeds mine by 200 damage, I have my 760 smite, and my 3rd Q proc, for a grand total of barely 800. Lee Sin Qs over the wall, dealing 20% missing health damage, plus his smite, for a grand total of nearly 1K, despite being a level down and steal the baron. I get blamed, naturally, despite being the only in position to even try and keep the lee out of the pit while no one is just finishing the baron
16.) Get choked out, slowly losing the game, after 40 minutes, despite having played perfectly for the first 10, and being totally useless after 15. My MF in a 0 minutes game does a grand total of 4K more damage than me, and in the end screen tells me it was my fault, and that I need to check the damage charts. In a 40 minute game, as Xin, with an MF Adc, who barely managed 4K more than me.
So yeah, jungle is nuts, if you're team isn't mentally handicapped. But when you spoon feed someone the game, and all they can do is drool on themselves and spit it back out, no, theres nothing you can do for players who don't know how to play the game, or when to just STFU and do as they're told.
You can play perfectly as the jungler for the part of the game where you're most relevant or impactful, and seriously outsmart and out play your opponent, but your team can literally just not listen to you, and theres nothing you can do to change that. The biggest threat to winning as the jungler isn't the other jungler, its the four people you're matched with.
And the big tilter, is that at the end they'll blame you despite having less XP, Gold Income, barely any more damage, more death, fewer kills, lower KP, and the wrong items. And the rest of the team will agree, because they didn't listen when you told them what to do, and you lost an unwinnable smite contest.