Why is a comma needed here?

Question

She would start applying to law schools soon and she wanted to know what the law looked like in action.

According to Princeton Review, this sentence is incorrect and to fix it, a comma should be added before and. But why?

Answer 1

Here are the general guides to comma placement between two independent clauses joined by "and":

When the conjunction joins two or more independent clauses, put a comma before the conjunction:

• The supervisor reported the misbehavior, but the personnel committee ignored the evidence and refused to terminate the employee.
  Commas and independent clauses

However:

There is an exception (there's always an exception): If the two independent clauses (compound sentence) are short and closely related, you may omit the comma:

• The assistants did the research and the manager wrote the report.
  Commas and independent clauses

It then goes on to say even if the clauses are short and closely related you shouldn't omit the comma if it creates ambiguity by doing so.

On the website Grammarly it says the same thing, to insert a comma between two independent clauses, and again mentions the exception:

But wait! There’s an exception. (Isn’t there always?) When you have two independent clauses joined together by and, most style guides say that it’s OK to leave the comma out as long as the two independent clauses are very short and closely connected. Here’s an example:

Arthur cooked and Melvin cleaned.
Comma before "and"

What exactly are and aren't short and closely related clauses isn't always clear, so as I said, in this case the comma placement is a matter of style, unless the placement of the comma changes the meaning of the sentence. I'm pretty sure they want you to place a comma here:

She would start applying to law schools soon, and she wanted to know what the law looked like in action.

Personally I don't see much wrong without it, but those are the rules most style guides hold to apparently.

Applying to law schools and wanting to know what the law looks like in action seem related to me, so it's possible the person considering that sentence incorrect thinks that the clauses aren't short enough, and therefore a comma must be placed. Also, style guides differ, so Princeton Review may have a different set of guidelines.