Cconfused...

Accurate is as precise and unchanged as possible playback of what the mikes picked up and got recorded.  Realistic is feeling like you might have been there, live.  Unfortunately, the two often don't coincide, for reasons already discussed above.

I look at it this way......

I hear on a system an upright bass.
If it sounds real and I mean I can hear al the subleties one hears when pressing down a string on a fretboard its resonance it gives....then attack and bottom and actual notes then it is an accurate reproduction. When rhythm and chord are accurate via accurate sound then you have a real reproduction of the bass.

Musicality is when the system jams...when it has actual soul in the sound....
Some digital stream systems are completely void of this instruments sound real but it has no "jam" to it...
There's the Bass the Guitar..etc...but it sounds like they are playing in seperate rooms....
Its like what some TV setups have in that HandyCam look the images are brilliant but the picture has no soul to it.

Nicely stated. 

So you have an excellant recording that we know of but sounds like dirt on a system...

An accurate system will tell you if the recording or mix was terrible...
Take for example some old Neil Young..

Better to listen to on an inferior system..

Neil could have done a much better job at presenting his music.