A conviction in 1996 is beyond 10 years so you do not need to reveal it on this application. The goal is seemingly to go back 10 years on the search.
In my area, criminal backgrounds entail the entire record.
But if this is an at-will position it doesn't matter what reason is used not to hire you. (There are some narrow exceptions). In other words, unless you prove you were discriminated against as a member of a protected class there is no legal recourse for a failure to hire.
This post is not meant to: 1) contain my signature; 2) contain legal advice; 3) create an attorney/client relationship; or 4) guarantee confidentiality.