Is Dr. Russo’s “endocannabinoid deficiency” a valid theory? There was a study published in Neuro Endocrinology Letters by Dr. Ethan Russo in 2004 that says many diseases being treated with cannabis correlate with an “endocannabinoid deficiency”, but I cannot read the study or find any more information about this. 

Are there other studies that can confirm or deny this? Or are there strong or weak arguments in Russo’s study that can help us understand whether it’s a valid theory?
I'd say it is a low-impact theory. The original (2004) paper in which this was proposed has around 60 citations in Google Scholar. That's pretty low for a paper like this (if the theory were influential). For contrast a 2000 paper on the monoamine hypothesis for depression (which is far from being the first paper proposing it) has around 460 citations and another one on the same topic from the same year [probably a theme issue in that journal] has 440, again according to Google Scholar.

There have been some reappraisals of endocannabinoid deficiency theory, e.g. in 2014 by different authors but in the same low-impact publication (IF &lt; 1) as the original proposal.

The initial propomotor of this theory has published his own reappraisal in 2016, but I can't even find the impact factor of this latter venue.

In general, deficiency in a given neurotransmitter has failed to satisfactorily explain any single widespread psychiatric disorder. For depression and the monoamines (serotonin etc.) at least here are experimental protocols to test the hypotheses (e.g. ATD), but the results are fairly mixed. Briefly looking at the 2016 paper on endocannabinoid deficiency theory,  I'm not even seeing an experimental way to test it like that. So it looks like the evidence is more circumstantial.