As far as scripture interpreting scripture, this wasn't even the case with the Reformers. When Luther read the book of James, it was an epistle of straw written by a Jew (this quote is quite famous), and wanted to "throw jimmy into the fire." He didn't attempt to use Paul to interpret the verses such as 2:24, he automatically disregarded their canonicity.

Calvin was no better, in his explanation of James:

Calvin doesn't use scripture to interpret this, he attempts to explain it away, saying either James got it wrong, or said he was just thinking we should be deemed just. You do not see references to what Paul says in scripture to harmonize the 2. These are just 2 examples of what "scripture interprets scripture" really meant to the Reformers. In reality, it was the person themselves who had the ultimate authority to interpret scripture. That's again formal sufficiency, the topic of this debate.

     How do Catholics show a correct interpretation, we trace it's roots throughout the Apostolic History, we use Scripture and Tradition to verify it, and just as the originals in Acts, ecumenical councils. It's not everyone get your Bibles out, and believe what you want to believe as Protestantism is.

     In the end, you are the ultimate authority, because if a certain belief system doesn't hold to your interpretation of scripture, being that as a Protestant you exercise private judgment, you are the final authority in determining orthodoxy.

     The Protestant will surely claim they are guided by the Holy Spirit, but so does the other person. Who decides who has and who does not have the Holy Spirit guiding them in Protestantism? There is no mechanism for them to determine this, it's what the individual thinks is right. If he disagrees, he starts a new denomination, and divides the body of Christ even more.