While it's true that some cells, e.g. pyramidals in the hippocampus can exhibit intrinsic oscillations, it's not true for most of the brain. Plus rhythms usually arise in networks, not single cells, and require the network to sustain themselves (that's why for example theta doesn't persist in vitro). Is there an example of a cell that can generate rhythms?
You are correct, single neurons are not intrinsic oscillators in vivo as far as anyone can tell. They could theoretically be -- there are ion channel combinations that would put neurons into an intrinsic oscillatory regime -- but that isn't really seen afaik.
Oscillations in the brain arise due to excitatory-inhibitory loops.
