From an ultimate truth perspective, one moment of experience gives rise to the next moment (to simplify greatly). Conditioned in the sense of 'tainting' is a modern addition to the Buddhist sphere from (behavioural) psychology. Since dhammas arise and pass away rapidly there is nothing that lasts that can 'slip into' another dhamma. It gives rise to another dhamma or it doesn't.
However from another perspective you are correct, if we say that one moment of experiencing contains within it all of the 12 links of the DO or that the highest moment of realisation contains within it all the eight elements of the noble eightfold path.
In any case nibbana being 'unconditioned' seem to arise from it being 'un-caused' (from a nibbana-dhathu perspective). But when you consider other ways of expressing the same thing (lack of lobha, dosa, moha) then calling it unconditioned by these things also makes sense.