I just don't assume that all Sunnis feel that ISIS represents them.
Not all, but a sizable majority feels that the ISIS represents them. The Sunnis were treated harshly by the Shiite dominated regime of Al Maliki. A lot of experts had warned him earlier and some even requested him to accommodate Sunni Arabs in his government. Al Maliki never listened to them. Now he is reaping the consequence of his arrogance.
Don't forget that a huge part of kurdish people are Sunni's as well and they are the ones who are fighting ISIS the most, it's good that you don't make assumptions.