I agree that finding out what was contained in your letters is a good idea in the event that you do not match. However, the approach mentioned above (as previously indicated) is unethical, dishonest, and down-right scandalous behavior in my opinion. It's a shame you felt the need to do that. It suggests a lack of confidence in yourself and your mentors.
Regardless of whether or not its in the Ethics Code itself is irrelevant. Simply because "the code" doesn't explicitly prohibit against a given behavior doesn't make it right. To justify your actions simply because "the rules don't say you CAN'T!" demonstrates an unsophisticated and immature understanding of the document and its intent.
BUT, if you want to get technical about then I shall refer you to principle C which states: "Psychologists seek to promote accuracy, honesty, and truthfulness in the science, teaching, and practice of psychology. In these activities psychologists do not steal, cheat, or engage in fraud, subterfuge, or intentional misrepresentation of fact."
And yes, I understand that "General Principles, in contrast to Ethical Standards, do not represent obligations and should not form the basis for imposing sanctions" . . . . "Their intent is to guide and inspire psychologists toward the very highest ethical ideals of the profession."
The appropriate way would be to ask your letter writers directly to view what they wrote.
And as for the comment about others not looking out for your best interest? Seriously?! I have no idea what kind of program you come from, but where I'm from I have 100% faith in my mentors and know - without a shadow of a doubt - that they all have my best interests at heart and do everything in their power to ensure that I as a student succeed to the maximal extent possible.