There is definitely some subjectivity. Language isn’t something that is easily parsed and scored. That is why they give examples on the actual report about the kind of biased language they saw, or whatever other issues led to the score given.
I don’t think they mean for their website to be the end all bias resource. More of a stepping off point for you to make your own judgments.
I don’t know if all states have it, but Virginia does have vote history on their voter registration page. It doesn’t show what your vote was, but does show that it was received and counted.