When are random variables random?

#1
I have an environmental dataset in which a treatment was carried out on a series of plots (situated on the landscape) in duplicate. However the duplicates also had undergone a treatment. This treatment was not replicated and therefore cannot be treated as a factorial design.

I have run into conflicting opinions on how to treat the data. One option proposed is to treat the secondary treatment as a random variable analyzed by a mixed model. However, this raises the question of whether an active treatment can be treated as a random variable. The other option is obviously that the secondary treatment is ignored, however, this drastically reduces the power of the test.

I thought I'd throw the scenario out to the statistical public and see what the response is.