The regulations simply require "the original or a copy", nothing more, nothing less and the copy is a plain old photocopy. Bringing the original might be best but a photocopy will work.
The State Department won't accept them for issuing a passport but they are still valid for use on a closed loop cruise, which only requires a government issued birth certificate attesting to birth in a state or territory (Puerto Rico certificates need to be issued after a certain date, one must look it up, because that territory passed legislation invalidating all certificates issued before that date due to rampant fraud).
Over the years questions have come up regarding these credit card sized ones, short form, long forms, and even hand written ones and all have been accepted as reported by the questioner.