Just caught up with this (look, I been busy, see?)
The Moorhouse reserve is owned by Natural England (aka English Nature) and hasnt been managed for grouse shooting for about 50 years - i.e. since they bought it. The main purpose of the reserve is research into climate change and there are alpine and arctic plants which are protected. There is free, open access to all of Moorhouse, but there are a few very small areas (exclosures) which are fenced off, mainly to prevent sheep from scoffing very rare plants. You can enter these fenced-off areas to look at the plants if you want. The reserve stops short of Cross Fell, however and an area to the North of Cross Fell has recent heavy investment for grouse shooting - in terms of new roads, buildings and butts. I wonder if this is what John saw. I'm not sure who owns this but its not Strathmore. Its all open access but parts of it are periodically closed just like anywhere else. You can walk wherever you want on Moorhouse most of the time, but you do have to watch out for mineshafts (There have been fatalities in the past where people have fallen down holes)
The Upper Tees part of the reserve (roughly East of Cow Green, plus Mickle Fell), however, is owned by Lord Barnard, The Earl of Strathmore and a couple of smaller landlords and is managed for sheep, grouse, water, artillery and tourists. This area is managed in partnership with these interests and a few large areas are closed to the public to protect rare/sensitive ecology.
I'm a voluntary guide for Natural England on Moorhouse and Upper Teesdale by the way... Initially, they were quite worried about Open Acess, but in practise there's been no increase in the number of people wandering off path or away from the ridges where, traditionally, there's been de facto access for many years.