My opinion: championship for the state does not = State Champion. Now that I know the reasoning from RS, remove the word "shoddy" since it was a conscious decision to include them on the list, and not an oversight or error in reporting - even though I personally disagree with the decision.
Invitational means restricted to those who have been invited to participate. When you run a private tournament only for certain schools based on enrollment, technically it's an Invitational Tournament. Ex: Campbell County has not been invited to participate in the All-A due to their enrollment. It's worth stating again the the All A is a privately funded, managed, and run tournament with no official KHSAA connection.