It’s true in name, but not necessarily in effect.
I was more particular to Dota, so that’s what jargon I’ll use. In Dota, the roles on a team are defined by resource allocation; the hero with the most resources is expect to have the highest impact on getting kills and/or taking structures, and most of the other players are an accessory to enabling them.
There are 3 lanes, two ‘full’ jungles (closer to each particular ‘safe’ side of the map) a few partial ‘hard’ jungles, a clockwork gold-rune spawn and then one ‘boss’ npc.
Since gold is (mostly) individual, and experience is split, it’s generally better to spread allies up as much as possible so teams typically have the ‘hard carry’ in their safe solo lane (towers in lanes are asymmetrical, so some are closer than others) a hero in their side of the jungle, one hero mid, and then two in the hard lane to try to pressure the enemy solo and/or jungle.
Now part of the catch of Dota is that different heroes have different power breakpoints, so different types of heroes have a time to potentially shine in the game.
The ‘hard carry’ usually has the weakest early game and needs levels and items to finally turn things around and win at the end of the game.
Some ‘semi carry’ heroes may only need a certain item, and a specific level to have enough skill or talent points to hit their stride (usually before the hard carry hits their mark) and then there are roaming/gankers that generally get most of their power from levels, but there may be one item they want to really do their thing.
Anyone else is pretty much regulated to buying needing consumable items (like wards to routinely maintain vision on key parts of the map, or counter-wards to find and destroy enemy wards, or dusts to reveal true-invis enemies) buy team-buffing items, and/or regularly buying the item that grants bonus experience.
The idea of ‘solo carry’ in Dota is that each role could feel like they had the most impact, per se. Obviously the goal of the hard carry is to have enough power to decimate the enemy team. However, if the hard support does their job right, then the enemy’s carrys will be weaker and get outclassed.
DotA allows players to ‘deny’ allied units, so they grant less gold and exp to the enemy team; lanes have a lull phase that’s predominantly focused on trying to out deny the other team, though over the years the penalty (or impact) of denying continues to be nerfed since competing to be ‘less weak’ isn’t as much fun as competing to be more powerful.
So while the power of the game enables one, sometimes two, heroes to accumulate a bunch of power to topple the enemy team, there’s still the basic reality that there’s 5 enemy heroes, 3 of which will generally be outside of your own impact, so any one of them can just farm more, gank harder, get more xp and denies outside of your own lane.
The idea is that regardless of how the other lanes go, that one person can still do what they can to not die, get their gold, and get an opportunistic kill (or boss steal) to keep things in their favor.
In HotS, the dps heroes are reliant on tanks and healers to protect them, but in Dota, heroes can get enough gold to buy anti-cc items so they’re literally unstoppable right-click killing machines. Or, alternatively, some heroes are so elusive that they can avoid the enemy team long enough to buy enough items to just outpush the other team regardless of hero kills.
So yea, the idea is there that a single player can ‘hard carry’ their games, but it’s also gonna take a lot of time invested to learn all the heroes, item combinations, multi-unit macro (gotta off-control a shared carried for transporting items between allies while also storing runes) and racking up enough mmr for people to be willing to allow said person to sit at the #1 spot.
Dota can be a bit better in players understanding their has to be given roles, and select heroes aren’t forced into just being that one role (cuz roles are based on who gets the gold) but it also does mean that uncooperative allies can undercut your teams ability to carry by ‘stealing’ gold and xp from the hard carry or semi carry heroes.
Tack on a couple other ability options that HotS has said they don’t want to do, and it’s also true that DotA has a higher potential for allies to grief/troll their team. Dunno how prevalent it is (esp with the ‘real phone id’ stuff for steam) but it has had its up and downs of being a concern at different ranks of the game.
Since a key part of the phases of the gank aren’t completely revolved around 5v5 action, some plays stand out more in Dota – such as long escape sequences, or chain ganks – because the balance of the game tries to essentially make every hero potentially OP.