I would say it a bit differently. It's about "affiliation". At state schools in football states, everyone feels affiliated to the state school because they live in the state. In NY, Syracuse is not even a state school so there is no auto-affiliation to it like in e.g. Alabama. SUNY was setup to be localized too so even SUNY schools don't experience that affiliation. In addition, there are a ton of colleges in the NE so a person in Albany who went to Union is not going to care so much about another private school he didn't even go to. I don't think it is about snobby... hell, the 25,000 locals that do support them and the basketball team are not put off by the elite snobbishness. By living in Syracuse, they feel affiliated.A lot of SUNY students (as well as locals and rest of state) have animosity towards SU and other private schools due to the fact they cater to wealthy and out of state students. A lot of people feel they are elite snobs and there is some truth to it.
It's a growing issue attendance wise when alumni can't be bothered to make the trip from the metro areas here and the alumni feel that the locals who have no ties to the university should show up just because. The school may be named Syracuse University but a more accurate name would be Cherry Hills University or WASP University of NJ/NYC/LI.
You may laugh or take offense but it's a huge reason that locals outside of the 315 area code do not attend and in many cases actively root against SU.
However, that's the whole point of marketing...to gain affiliation. They need to market better to the community, surrounding area, and to alumni. Recent alumni have no affiliation to the football team.