A graphic for Random intercepts via distributions

Good afternoon,

I came across a picture (https://github.com/hkil/m/blob/master/mlm.PNG)
that tries to show the concept of random-intercept models using
distributions.

I think, however, the picture erroneously mixes regression concepts (e.g.,
error terms) with distributional properties of those regression concepts.

I appreciate confirmation from the expert members?

Thanks,
Simon