Intermediate level can possibly be 'high level' in certain ways - depending on situation. Some can be high level -- even though they say 'intermediate' level.
And we have to consider that 'high level' (and fuzzily mixed in with 'intermediate' level) can be quite broad - and needs to be defined for a particular category, or for 'overall'. For example - as it is a big world out there, with lots of people -- there are different/various forms of high/intermediate level.
I personally think that - after developing adequately in certain ways (not just in piano playing, but also in music - theory, composition etc), we all get to some 'high level' - our own form of high level (and/or intermediate) in piano and music.
It doesn't matter much to me what level I am overall. What I mean is - after enough time - practice, learning, developing, aural training, intervals recognition, music memory, analysis, composition work etc -- people eventually know and have a feeling -- or just really know - they have reached some 'special' level. Everyone is different. And has their own special level after enough development. Their own high level. The usual journey is to become more and more 'at one' with piano, and with music.
I'm not a 'beginner' ... as in absolute beginner. But I recall very well the times when I was an absolute beginner. They are special times. I love the feeling of not being able to do certain things, and love working toward learning and developing, no matter how long it takes ... as in years and years etc. This is probably the same for lots of people. The fun and enjoyment of developing. The fun and enjoyment of playing piano, and music.