I suspect that this due to some confusion about the meaning of "AC'97"
Here, thanks to Wikipedia is a picture of an Esoniq AudioPCI 97:
Observe that on that card are two major chips - one is the AudioPCI chip itself, and the other (made by AKM) is the codec. AC'97
doesn't specify any programming interface for software (After all, from Intel's perspective this was entirely related to motherboard onboard sound and they don't care about competitor's motherboards). What AC'97 specifies is a protocol for connecting audio interfaces to a codec, and the capabilities of that codec. Hence the name - Audio
Codec 97. The primary idea was to standardize an interface that Intel could implement on their chipsets, and that codec vendors could implement on their codecs, to make motherboard onboard sound as cheap and simple as possible, without major supporting chips.
AC'97 does define some programmer exposed registers, yes,
implemented by the codec. But it doesn't define a full programming interface - this can be considered similar to the defined MAC registers for Ethernet. In fact, there are large parallels here - in both the case of an AC97 codec and a MAC, you have an interface which converts between signals the host can handle with the outside signalling format (in the case of AC97, analog and maybe S/PDIF)
So the AudioPCI 97 is an AC'97 device in the same way as your average ethernet controller implements an interface like MII to talk to a MAC - this is the interface used to talk to the analog components. The codec in the above picture? Yep, that uses AC97
(Side note: The other purpose of AC97 was to support technologies like the AMR - Audio and Modem riser - and CNR - Communications and Networking riser - which were designed to make motherboards cheaper by moving the analog/high frequency components which must be certified onto a separate board. As you might guess from the absence of them from any modern machine, they were unsuccessful because (a) modems were almost obsolete soon after they came out, (b) AMR/CNR modems were less compatible than PCI modems and so ended up not any cheaper, (c) AMR/CNR could only support softmodems, and (d) codecs came down in price, and (e) very soon onboard ethernet and audio became so essential as to defeat the purpose)