Like you Flour, my gut feeling and instinct tell me the same regarding the EFL and the big clubs in League 1. However, I've spoken to TS a couple of times (on the golf course) and he says we have an excellent relationship with the EFL and an even better one with the FA (England Ladies playing at NYS etc).
The impression I get is that under Boothy (and the owners after him) we were very much seen as a paria club. On the outside looking in. Stale, boring, outdated. Under TS bridges were built with the EFL and the FA (starting from when we had to move from the DVS back to Rotherham. The EFL would not have kicked us out of the league if we didnt meet the 4 year deadline as long as progress was being made on the new stadium) and we are now viewed very favourably and as a progressive club using a model for others to follow.
Despite what we think (and I too get those feelings sometimes) the EFL and FA quite like TS's RUFC.