Interesting, I have never come across such a local rule. Can you offer further information on what your words "in such circumstances" means or are you suggesting the R&A is sympathetic to any specifically named stakes, ropes and poles being defined as stroke not to count if a ball contacts them? My sentence "There is no rule that allows that and no approved local rule that enables such relief from normal course marking stakes and poles" is simply what the R&A has published. If you have advice that contradicts or extends what they have published I'm interested to hear detail of any advice they have provided.
The opponent in the OP apparently claimed relief from hitting some ropes as a matter of course. I presume you would agree no such assumption can be made.
I agree with you last sentence.
Re the R&A's confirmation.
We have a couple of greens where players are tempted to cut between the green and a nearby bunker with a trolley. This was causing some significant wear and tear during the winter. We temporarily placed some closely spaced short red and white stakes between the bunker and the edge of the green. We had intended to use the LR re obstruction within 2cl etc but realised that some stakes were more than 2cl away. Further, when chipping from short of the green, balls had to negotiate the 'wall' of stakes. Occasionally a ball would be diverted into the adjacent bunker.
The R&A suggested TIOs but we thought that the relief procedure was too complicated without a referee and suggested E-11. The R&A accepted that in this situation that E-11 was a reasonable (I don't think they actually said equitable) solution provided the stakes and their location(s) were clearly identified in the LR.