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 have some points to consider but there are also a deep explanation to it, the price is affected when the market is going to some correction. And is going back to its up and down not stable price, and these twitter, facebook, etc is just a tool to introduce the capability of what crypto can do and can help into an economic aspect.