Unfortunately, it is possible that the birth was never registered. Home births were much more common way back when, and sometimes they just ignored all that pesky paperwork. In addition, many immigrants did not know the proper procedures or could not communicate the event to anyone. Also sometimes, I'm told by my grandmother, Grant Aunt Ethel died at home, so the family just planted her in the back yard. Okay, ewww. Anyway, no death records. It's also possible that the records were lost - case in point: the 1890 U.S. Census records were destroyed in a fire. Another problem is that people just didn't know or remember when a person was born. You will see an 1870 census record where Great Grandma was listed as 17 years old, but 10 years later in the 1880 Census, she's now 31. Again, language barriers can be a problem here.
I agree with the earlier post that it is often necessary to retain a copy of the original document because it usually has extremely interesting information that isn't shown on the report. But a photo copy or digital image will do just fine unless you are the executor of that person's estate.
Good luck and happy hunting!