That is quite incorrect. Market makers are typically close to flat and are trading liquid instruments (assuming on exchange MMs like NYSE DMMs). The tail risk on a short duration trade of an exchange traded instrument is quite small, especially if the MM is not writing put options which this specific quote refers to. When writing a put option the premium collected by the writer is typically not enough to compensate for tail risk. Thus there is limited upside with extreme downside in the face of a tail event. Also the options tend of have longer durations (months or years). Firms pursuing this type of strategy are typically carrying a lot of mispriced risk on their books for a long time.

It might be true if you are talking about market makers that have an advantage over other participants due to regulations. However nowadays market making on liquid instruments is almost equivalent to high frequency trading. The tail risk might be low if you have very low latency and perfect connection to the exchange. Anyway your pnl distribution will be negatively skewed. You are unlikely to lose tons of money like Knight (their testing algorithm kind of actively tried to do it) but making a steady profit is not easy in liquid markets.