I was initially commenting on the PA thread, yes, Roussette, but decided there was little point in continuing to do so, as many of the posters on that thread were quite convinced they knew everything that was necessary to know about the law in this area. 
What I’m saying in relation to this study (and I don’t dispute that they did a lot of work on it, at all) is that they set out a wide-reaching aim: “to help charities make evidence-based management decisions about whether to seek and retain Royal patron”. It then makes it clear however that the sole outcome that is analysable and comparable across the wide set of charities which have Royal patronages is revenue, so they used that.
Having picked that as their sole focus they acknowledge “we could get no clear answer on the effect of Royal patronages on charities’ revenue. This is because charities’ revenues are very jumpy and uncorrelated with each other, which meant that our various analyses returned answers that were either obviously implausible, or had huge ranges that included both negative and positive values”
They also openly accept a number of limitations inherent with this approach - for example, their conclusions about having a royal patron “may omit important elements of work behind the scenes, but no information is available about that”.
Given this, I find their headline “Royal Patrons don’t seem to help charities much” a bit eye raising. “Seem” is doing a lot of heavy lifting in that sentence!