The Fur and Feather guide really stems from the fact that the .22 at such low velocities can feather plug on soft feathered birds such as pigeon. The plug effect can stop penetration to only a few mm's which when on a full crop is not enough to kill the bird outright. Often a pigeon will fly a 100m or so before dropping dead, if it drops dead at all.
The wound track between .177 and .22 isn't that huge a difference. Over penetration makes little difference as its the track wound that does the damage. At these low energy levels then there is little energy dump effect. Which is why perfect shot placement cannot be over emphasised as it is the most important for any successful outcome.
Deliver .177 or .22 with precision and both are equal. The .22 may stop faster but they can over penetrate too, there being so little in it all. All arguments are about marginals that make very little practical difference. I tend to use .177 due to its flatter trajectory and I've never known them to feather plug. However, the .22 "smack" is quite forthright in its own way.

Higher velocities everything changes. 12ft/lbs rifles are just enough for their intended use within the farmyard, which is why we have them.
Lastly, we now have the tools to head shoot consistently, which wasn't always the case 40 years ago. No longer is a central hit and farm dog to finish the job off enough as we can now do better than that.