Examples:
Anthony Spencer will need microfracture surgery, and is done for the season.

What Has 4 Letters, Loves Making Laws, And Is Trying To Ruin Our Country?

Coal generates 44% of our electricity, and is the single biggest air polluter in the U.S.

My understanding is that you it is okay to use a comma and the conjuction "and" in a series/list and to join two independent clauses. But the above examples are neither a series or independent clauses, yet I see this usage all the time.

Is there an exception to this rule and if so, what is the exception?

After some research it appears these sentences suffer from the phenomenon of pronoun dropping which is okay in informal writing. I think?

Anthony Spencer will need microfracture surgery and is done for the season. [correct]

Anthony Spencer will need microfracture surgery, and he is done for the season. [correct]

Anthony Spencer will need microfracture surgery and is done for the season. [wrong]

In all conventions, it is normal practice not to use a comma with a list of two items, which is what you have in the last example. However, for clarity, some writers like to add one. (I don't think that's such a crime.)

Confusing. Your first sentence and last sentence are exactly the same. Yet you say it's correct and wrong. Which is it?

Anthony Spencer will need microfracture surgery and is done for the season. [correct]

Anthony Spencer will need microfracture surgery, and he is done for the season. [correct]

Anthony Spencer will need microfracture surgery and is done for the season. [wrong]

I think GM intended that the second (incorrect) version of the identical sentences be "... and he is done ..." I don't know whether GM is correct; I suspect usage allows some freedom of choice on this. My own approach would be to follow speech, where I might pause if I wish to indicate that the second was not an automatic consequence of the first.