In living systems which exhibit cumulative adaptive evolution, you need to have some sort of a signal that passes largely-intact down the generations - otherwise existing adaptive complexity is not preserved and the system exhibits an error catastrophe.
This is the basic point that talk about high-fidelity transmission is usually attempting to get across. Of course, high-fidelity information transmission can still be implemented in systems with low-fidelity copying by using some kind of error correction technology. That is just basic information theory. Shannon covered this, as did von-Neumann in "Probabilistic logic and the synthesis of reliable organisms from unreliable components" from 1952.
How and why various researchers got into a muddle about this point is still not entirely clear.
One culprit appears to have been the late David Hull. Hull apparently attempted to reformulate evolutionary theory around the idea of copying of "structure" which leaves it "largely intact" - with a confused-looking and potentially-misleading presentation of the topic in "Science as a Process". Memeticists should probably publicly distance themselves from Hull's apparently misguided effort in this area.
Boyd and Richerson (1985, p. 266) say:
Richard Dawkins forward to Blackmore's book gives a particularly clear example of how important the high fidelity of transmission is taken to be by Dawkins at least.My reading of pages x - xii there is that Dawkins is fending off the criticism that mutations obliterate any inherited signal, rendering an adaptive analysis redundant.
Perhaps Dawkins' presentation was partly to blame - though many seemed to manage to successfully understand it.
Dawkins did actively cause problems in being understood by redefining the term "replicator" without including the usual implication of high-fidelity copying. I can imagine how that might have caused misunderstandings.
Alas, most of the other hypotheses I can think of to explain how this situation arose are more uncharitable ones.
The result has been a rather unpleasant 25-year old rift between workers in closely-adjacent areas of cultural evolution. Er, shouldn't we all be working together?
- Tim Tyler (2011) The claim that evolution doesn't require replicators