The distinction being made here between the content standard and a strategy for showing that standard IS the crux of the problem for CC.
The tests could be made to test only for the concept, but are much more likely to be made in such a way that you have to know the specific strategy meant to "scaffold" you to the concept, rather than be secure in the concept itself.
It reminds me of a district level math supervisor when my oldest kids were in elementary. The district was using EDM (I know, I know, it was actually great for my kids and did what it was supposed to do, but I did realize as the years went on that it really didn't work for 50+% of their classmates).
The supervisor was explaining how they were trying to make sure that every teacher was really using the curriculum in exactly the way prescribed. It had clearly come to their attention that some teachers found the program lacking and were modifying it.
Their solution? They were making up district-wide unit tests for the lower grades that would ask the students specific questions about the games and activities that were to be included. That is, besides some questions that actually tested the concepts the kids were to be learning, they'd also have questions that tested whether they knew how the games were played, or what the rules were for playing them.
So, now the students were being tested on...nothing...so that the district could ding the teachers/school for it. And that, in a nutshell, is also the big problem for CC. Instead of asking questions that determine if they know and are fluent with their facts to 20, they are instead going to design questions that try to tease out HOW they were taught them and ding those who didn't use the specified "strategies."