The modern CPC are a very friendly bunch I have no doubt and have moved on from the days of the song quoted above - as we all hopefully have. So although CPC clearly stated in their OP a requirement to have insurance in order to cave with them, other members since then have suggested if you just go up there you'll find a more 'progressive' attitude. That's just great.
Unfortunately, whether you like it or not there are subtle politics involved here which relate to freedoms of access for all. CPC (and BPC for that matter) are fairly self centered when it comes to dealing with the estate as their big fund raiser, the winch meet, is reliant on a good business relationship with the estate. It is not surprising that they are willing to agree to conditions which allow them to achieve this going forward.
The rather unfortunate side effect of this is that it encourages the representatives of the estate seek assurances that all cavers are covered by insurance. This might not be an issue for those in clubs who do have the BCA insurance but it is an issue if you happen to represent all cavers as CNCC do. If you are in the club system it is not always easy to see that many others do not cave this way or wish to and restrictions like we had in the past are not good for the future of our sport.
Someone who is involved in 'politics' will have to spend a lot of time trying to sort this out in order that we don't take a step backwards in Dales caving. So it is not the trivial issue that some suggest it is.