Hi Fred
In stretched data, the PSF varies with brightness (eg bright stars have different FWHM than dim ones). As far as I can see, deconvolution will not work properly if you cannot define a consistent PSF.
According to Ivo on the StarTools forum:
As of version 1.3, the difference between linear (for which screen stretching is needed) and non-linear data has been abstracted away; all operations now *appear* non-linear, but some are, in fact, performed on linear versions of the data in the background. StarTools accomplishes that by 'going back in time' while your data was still linear, applying the operation to that version of the data, then calculating how the result would have looked after all the steps you performed after you decided to apply the linear step; it's akin to time travel where you change the past in order to change the future.
What this means for you is that you don't have to worry about keeping your data linear for, for example, deconvolution - you can now apply mathematically correct deconvolution any time, for example after stretching, HDR optimisation, Wavelet Sharpening, etc.) - it will still work! StarTools will calculate the result for you as if you performed deconvolution before you applied stretching, HDR optimisation, Wavelet Sharpening, etc. Neat hey? It's ultimate freedom! And not to mention much more user friendly... 
I guess that what this means is that StarTools does not actually do deconvolution on stretched data. It will not allow deconvolution on data that is imported in a stretched form. It protects you from making a mess of your data by cleverly referring back to the linear data if you wish to apply deconvolution after stretching linear data
in StarTools. Other packages are not so protective or flexible and, as a general rule, deconvolution should not be applied to stretched data - it won't work properly.