Usually, the devil is in the details, but in this case the devil is in the lack of details. That is, you've shown one graph among dozens in that article, one that showed an example of SSD tweaks and using AHCI that caused a performance decrease in the SSDs, while others in the article (not all) show a performance increase. An important detail about the Intel SSD, which has a page dedicated to it in the article, is also missing from that single graph.
The potential problem with this article is if one tweak has a negative affect, then some people will see that as "tweaks are bad... AHCI was a tweak... AHCI is bad...", not that one in particular caused a problem.
The Intel SSD in the article does not "like" having "Disable write cache buffer flushing" enabled, one of the tweaks used in the testing. That setting did not affect the other SSD being tested much at all. The difference in performance with that setting disabled for the Intel SSD is significant to huge in all cases, and all for the better:
A simple description of NCQ compared to the lack of it is this:
No NCQ: OS file system sends one I/O operation in one request to a disk drive, and can send another when the drive acknowledges it has finished processing that request.
With NCQ: OS file system sends up to 32 I/O operations in one request to a disk drive, and can send more as soon as the drive acknowledges it can process more requests.
Another analogy is if I handed you 100 sheets of paper, one at a time, or in stacks of 32 sheets at a time. The latter can be accomplished with four movements of my arm, while the former takes 100 movements of my arm. The overhead in the communication protocol between the file system and the drive to perform 100 operations or four makes a difference.
Besides that, a SSD can process I/O requests in parallel, doing two things at the same time. But it can only do that if it has more than one thing to work on at a time.
I can't see a situation where NCQ, provided by AHCI, reduces a SSD's performance.