I'm not talking about Jarrett. It's the "just" that gets me here. As in, "oh, I'm just sitting here watching tv..." Takes a LOT of work to improvise at a high level, just as much work as it would take to become a great composer. In the moment, it may seem to come easily, but the homework has to be done first.
For the purpose of this thread, Hardbopjazz is defining composition in the narrow sense of tunes, songs, pieces ... things that you put your name on and give a title to. More broadly, we can say that the use of any preconceived music, such as licks, lines, patterns, melodies, specific chord voicings, etc., would constitute compositional playing. Most of the improvised solos that we hear in jazz contain various degrees of compositional playing, though usually not in the sense of being through-composed. That's what we call the Jazz Language. There's no value judgement here, but for the practicing musician it is a distinction worth making.
So for example, Oscar Peterson didn't write many tunes, but in order to play fast and continuously as he often did required him to have lots of patterns, licks, and lines well-practiced and at the ready, and to be able to work with them on the spot.
Jarrett has a bunch of tunes in the first Real Book, so we can say he's done all three: composing, compositional-improvising, and pure improvisation.