What is interlineation and what is its significance in legal doents?

I'm trying to correct my middle name on my Birth Record, which was written only as a middle initial. From my understanding, an incorrect information on the record will be interlineated (a line will be drawn across the incorrect info and the correct info will be written on top). However, I was given a reply by the state agency in charge of amendments and it stated that currently the first and middle name on my Birth Record is blank! How could this be, if the legal way is by interlineation and not deletion? Is there some white collared illegal activity going on the state level or what? Please shed some light on this and include any related information or similar experiences. Thank you.