Does the mechanism of the Schmidt reaction involve a nitrene as an intermediate? Per the mechanism described here the reaction does not involve nitrene as an intermediate.(EDIT-1---I initially thought the written mechanism described so, but as Zhe points out,I was wrong in my observation.) 

But, can anybody shed some light on why the reaction does not involve nitrene; though it possibly can?
Nowhere in that link is there a nitrene formed. All steps are concerted, that is, you see that alkyl shift happens at the same time as dinitrogen fragmentation.

So indeed, nitrenes are not intermediates. I suspect that mechanistic studies have been done. You might consider looking at this paper.