The notion "As cells develop some genes are turned off permanently." is partially true and partially false. In normal developmental process, some genes may be off and other genes may be on leading to cell differentiation. The differentiated cells do not produce any gene regulatory proteins to turn on the genes that are specific to mother cells (earlier cells). The differentiated cells now produce their gene regulatory proteins to turn on their own specific proteins.
For example, the ectoderm-derived skin cells express keratins that are specific to skin cells. The same origin of neuron in the brain produce neurofilaments that are specific to neurons. Thus, neurofilament and keratin genes are permanently off in skin cells and neurons, respectively. The notion is true.
When cells are damaged in some fish, amphibians and reptiles, parts of the wound-surrounding tissues then de-differentiate (escape from the state of differentiation) or trans-differentiate (turning their direction of differentiation into other cell lineage) due to many extrinsic ques (largely unknown). The ques may recover the earlier gene sets that are responsible for keeping different state of cell lineages to be transcribed and translated, leading to dedifferentiation or transdifferentiation. The notion is false.
These phenomena are called parts of reprogramming the genome. In-vitro manipulations involving cell fusion between different cell lineages, cloning by microinjecting somatic cell nucleus into the oocyte, and generation of induced pluripotent stem (iPS) cells by transfecting pluripotent transcription factors into any somatic cells are all enabling technology that turns dead genes on.