Yeah that's how I remember it too. In one town we lived in, we always got videos from the independent place. My main memory of Blockbuster is that one time my parents went there instead, and they gave us the wrong movie, which my sister and I were very disappointed by.

In another town we lived in, the video rental place was a local chain with fewer than 10 locations, maybe just around 5. I don't remember if a Blockbuster even existed locally.