Index arbitrage is a mechanism that corrects mispricings between an index and its constituents. That isn't the mispricing being discussed. What is being discussed here is the potential for the prices of individual stocks to deviate from any reasonable level because of their inclusion in an index.
To some extent, it's just a matter of supply and demand. Because so many people are investing passively, inclusion in an index with highly traded ETFs can cause huge demand for a stock that no one would have particularly cared about otherwise. There are tons of examples of this around the Russell indices, but stocks in most popular indices carry higher multiples than similar companies outside of them. There is also what George Soros called reflexivity - this increase in stock price makes it more likely that your business will survive because it makes financing the business easier. A large market cap both means you can issue shares cheaply, and it makes banks more likely to lend to you. That helps the business stay alive, but it doesn't necessarily improve their underlying business. Without anyone fundamentally evaluating these companies, such situations can persist indefinitely. Short selling is also made hard by the heavy demand created by additional inflows to these indices. Even if you identify a mispriced company, its continued inclusion in the index might prevent the price action that would remedy the situation.
In the end, I don't think this is the end of the world, but there is the old saying that bad money drives out good. This kind of mania makes it hard for normal feedback mechanisms to function appropriately. The most direct costs will be born by those who invest in such instruments, but it also adds greatly to the correlation of the markets, since price movements are now implicitly tied to inflows of money from markets.