Imo a program is just a name and any program can be turned around given the right resources and people. In reality that is not always possible of course especially due to financial resources, available facilities, location but in theory for example the 2014 Vanderbilt team has nothing to do with the 2020 Vanderbilt team except that the tradition gives them an edge in recruiting.
Don't get me wrong, there is a reason why some teams are consistently successful but that doesn't really have anything to do with the "legacy" of the program other than that legacy creating financial resources as well as attracting good players and coaches.
One of the worst examples of this is when there is a soccer world cup and the announcers try to interpret stats from past tournaments. Like when germany plays England and they say Germany leads the head to head in world cups 4 to 1 over England. That really means nothing since none of the players who contributed to the 4-1 record is still active.