Sometimes they are not erected for months or even years. Also, stone carvers made mistakes. There is a stone in a cemetery in downtown Tampa, FL, on which the stone mason made a mistake in the spelling of the deceased's name. He apparently returned to the grave and struck a diagonal line through the incorrect letter and then carved the correct letter above. Always seek corroboration for everything you see on a gravestone.
Some documents can be both primary AND secondary sources.
Death certificates are notorious for their errors. The only primary source information on the death certificate is the date of death, and sometimes even this is incorrect. Always examine the date of death and the certificate's issue date. If there is any significant time lapse, look for other corroborating evidence elsewhere. Also, the date of birth, birth location, age, names of spouse, and names of parents are all secondary sources.