The CAR was last updated in May 2015. It is frozen in time since then.
For example, German Cathedrals or The Labyrinth are not included... Or any clarifications from 10/2015 or later, of couse.
In this case (scoring fields with barns) is almost okay, but you have to read pages 65 and 66, or you will be misled as @ny1050220 pointed out.
Both pages contain a scoring summary covering all cases (cities, castles, pigs, pig-herd) except sieges, which were omitted. However, you may find the full picture in pages 212 and 214.
When creating WICA, we used all the info contained in the CAR and tried to polish some outstanding issues, like this one (or the interaction of the dragon and the school, that wasn't consistent across the document).
You can find a summary of the scoring of fields with and without barns here:
https://wikicarpedia.com/index.php/Abbey_and_the_Mayor#Scoring_summaryLittle Buildlings are not considered in these summary (or Markets of Leipzig since they apply only to fields at the end of the game and not barns).
And yes, barns can be used for good... or for bad.