Sample independence

I have a simple random sample study design in which I randomly selected 1X1 mile sections and around these sections I randomly placed 3 points. At these 3 points I collected data such as percent shrub cover (factor variable with 4 levels) and counts of organisms. I would like treat these points around each section as independent and conduct a generalized linear model analysis.

My sample size is over 4000 points that span a large study area approximatley the size of the state of Kansas.
Is it ok to assume spatial independence between these 3 points around the section and carry out a GLM analysis.

I would appreciate any input.