Alex, you clearly don't understand the situation and maybe that isn't your fault. Maybe somebody should have explained how delicate the access situation for this cave is.
Alex has not told the whole story. Apparently, what he did was make a video and post it on Youtube.
Let me compare this to another scenario. Our village has an open gardens weekend every year. The organisers ask people to open their gardens to the public for a weekend. Imagine if you obliged and then somebody made a video of your garden and surroundings including you house doors and windows and put it on Youtube along with your address. I didn't see Alex's video but I can easily imagine that there might have been things in it that really annoyed the landowner.
The landowner wants to maintain a degree of control over who goes to the cave. The landowner is prepared to allow access for responsible, experienced cavers only. They have been very generous in allowing access with minimal conditions. They could have insisted on a gate or they could easily fill it in. They do not want the cave advertising on Youtube and that is easy to understand.
Alex is too young to remember what happened at Dale Barn Cave where the cave was filled in and the entrance totally obliterated.
Alex, you made an innocent and understandable minor error of judgement. You took down the video when asked. Hopefully things will be smoothed over and there will be no serious damage to the relationship with the landowner. Don't do anything to make things worse.