Suppose the price indexes are adequately measured and there are no problems regarding the data in itself. By my experience, using a sector price index -- for the industry sector that you might be analyzing -- is more adequate than a more general price index for deflating the series. But there could be a situation in which it is more adequate to use a more general price index than a sectoral price index for deflating the variables?
If your analysis is trying to provide predictions for the particular sector at hand in isolation, then one would ask why would you go for more than the index for that sector. However, one then notices that your index is the most comprehensive one possible for your research due to the isolation.
The last point brings one to ask the question of what happens whether the analysis will need a different index if the aforementioned isolation is relaxed. In that case, it is highly likely that you would need to change the benchmark index depending on the purpose. For instance, if a capital owner is trying to find a sector to invest in, it might be in his best interest to see how different sector are doing with respect to each other (or a benchmark) to come up with a better educated decision. An equivalent concern would be subsidies for instance.