You're 100% correct, though some of his sitting on the toilet thoughts might not make it to the public. What the news, when its being done correctly, does is provide surrounding context to interpret the remarks. This is valuable even for normal politicians as, it bears repeating, it is impossible for the population as a whole to be informed on every issue, and most people aren't informed on even a few. Low information constituents will misinterpret remarks without context.

It also encourages him to publicize views that can withstand press scrutiny. The outrageous stuff we see on Twitter might have been self censored if he had to tell it to a skeptical press that will place them in context.

Prior presidents have been very circumspect in what they say, which has reduced the pressure on this point. Extreme situations pressure us to discard gray areas. In order to maintain a healthy civic discourse, we need everyone to cooperate more and be more generous to the other side, but this can't be done unilaterally or you just get steamrolled.