Twitter is just a part of media like print / electronic or social media including Facebook; linkedin ; You Tube etc. And each type of report on any type of media has effect on the price of bitcoin. When there are positive news the price goes up and in case they spread negative news then the price falls.
You're right. But not only Twitter but also Facebook. Telegram, Reddit, Youtube and others kind of social media can affect to the price of bitcoin. Bitcoin's price will go up or down depending on the negative or positive news of bitcoin.