LoL is taking a different, and largely more conservative approach. I assume this means Riot plans to build upon League of Legends for...a decade? Maybe even more? That is to say, we should never really expect a League of Legends 2. Instead, we would expect to see engine updates, visual enhancements that reflect better baseline hardware over the years, and continual content additions.
The only flaw in this approach is that the game is entirely dependent on Riot. If Riot imploded, there would be no way for players to continue playing the game.
Also, Dota 2 won't have a problem with the crowd funding. The game is only a fraction of the size of League of Legends (player base), so there is plenty of room for them to continue to grow. Further, the items they offer for the crowd-funding rewards continue to provide killer value for those who buy them. There's no reason to assume that the Dota 2 population won't continue to grow or that Valve will stop providing good value for Compendium purchasers, so there's no reason to assume they won't see $10,000,000 annual prize pools. And regardless, TI has a base line of $1,000,000.00 which is always there. Everything else was always just icing on the cake. But it creates community, which is something Valve has proven themselves to be extremely adept in creating and understanding the value of. People feel like they're a part of something in Dota 2. That will give the game a quality of life atypical in gaming.
That said, their assertion that Valve is "begging" anyone is either a gross misunderstanding of how Valve's TI economy model works (which would be a pretty embarrassing revelation, as that company should be closely examining the business models of competitors to see what they can adapt to their own model), or it's unconstructive PR dodging. Either way, Riot needs to do better than that.