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PCASA/Accugrade has been around a while and purports to have the patent/trademark for the holder and grading scale other grading companies are using (including PSA).
Does that mean you should trust ASA? Go to their website and judge for yourself. I could not find any guarantee on the site, or what cards they refuse to slab, etc. (I did not look that hard, so that information might be there, somewhere).
http://www.asa-accugrade.com/index.php
I have two ASA graded cards in my entire collection, both low dollar 70s hockey purchased several years ago. I have (obviously) avoided ASA, and will continue to do so for vintage and other high dollar items.