Hi AG, in jazz and popular music the bIII notation to a chord is useful to indicate we are playing in a major key and there is a modal interchange with the parallel minor key. There is not really a standard way to chord notation in jazz, but as you get yourself into it you start to get familiar with this types of notations. In this case the bIII chord notation doesn't fit completely in the context but it gets the work done, so it isn't actually a mistake.

I had never thought about it this way, Very interesting question @A G and answer @Sebastian Gonzalez