Putting the cart before the horse: to state a claim without proof then prove it later or use a worse method?
(I have turned my comments into an answer).

Whether or not to discuss statistical assumptions depends largely on the nature of your work. Many authors of statistical textbooks and manuals discuss assumptions in great depth. They also highlight the importance of reporting the results of assumptions testing in your manuscripts. In my experience, this is very rarely done for several reasons. For example, results are often the same regardless of assumptions (this is not always the case), if you are reporting statistically significant results and effect sizes then perhaps the need to discuss assumptions is less important, word limits often restrict the ability to discussion assumptions, and it is often very rare these days to find discussion of statistical assumptions. Note that these points relate to applied journals and papers. If the paper is statistical in nature, or you have non-significant results and need to highlight that your statistics were appropriate, then perhaps discussion of assumptions is warranted. I very rarely run across discussion of assumptions for statistics ranging from t-tests to survival analyses and latent growth modelling etc. In statistics papers though its often important to highlight what assumptions are needed and such. 

I have published in the pre-eminent journals on pain and you certainly do not need to discuss assumptions in them most of the time. If you review recent papers you will see that these assumptions are very rarely discussed. A simple "we did regression" and "here are results of regression" will suffice (with more elaboration, of course!).