For some discs, this is true. For example the NIN Downward Spiral contains different mixes for the CD and 2-ch SACD layers. But this disc came out as a CD first and a SACD later. in general, why would a company that intends on releasing a SACD first spend the time and cost to create more than one mix? I would expect most recordings are done in analog or high-resolution PCM (e.g. 24bit/88.2khz), mixing is done in the same righ-resolution format, and then the final master is converted to either 16/44.1 or DSD (or both) for the final disc. This seems especially likely for classical music.
The Norah Jones SACD is an interesting disc to read about. For the 2-channel mix, they took the 16bit/44.1khz CD format and converted it to DSD, rather than going back to the original source. People noticed.
With anything that is not a new recording, there will be an old mix or mixes to use, so it will cost nothing to use one of them for the CD layer. Often, in the material in the case of the discs that are sold, they even tell you that they are using an older mix for the CD layer, and have only remastered it for the SACD section.
In the case of new recordings, there is a reason to do a second mix, which is to promote the SACD format, so companies want that version to sound better. Think about the fact that there are companies making the discs, and how it benefits them if people like the new format. I doubt that Sony has ever released a hybrid SACD with the same mix on both the CD and SACD layer, though obviously I cannot know that for sure.
Also, it isn't going to be as expensive to do two mixes at once as it would be to do two mixes at different times. They would save time by needing to load the source multitrack tapes only once. Indeed, it could be as simple as just adding reverb to one of the multitracks for one of the mixes, or simply re-EQing the mix for the CD layer, to slightly diminish the deep bass and treble (or whatever). That would cost practically nothing, and would serve the purpose of promoting the new format.
Of course, there could be hybrid SACDs with precisely the same mix for both stereo SACD and the CD sections, but there will generally be no way of knowing that.
Really, though, all they need to do is have the SACD layer at a very slightly higher volume, and then when people compare, because practically no one bothers to level match things, people will believe that the SACD has better bass, better treble, and will reveal more detail. This is because human hearing is not linear, and as the volume decreases, subjectively, the bass and treble appear to diminish faster than the midrange, which is why they put "loudness compensation" switches on so much vintage gear, to compensate for this well known effect. And of course, being slightly louder, one will hear more detail, so the purpose is served well enough if only they have the volume slightly higher on the SACD section(s).
That aspect of human hearing also tells us what is fatally wrong with most of the casual comparisons that most people make, when they are trying to decide if two different CD players sound different or not, or two amplifiers, or two of anything, really.
And as a side point, several of my relatively new SACD recordings were DSD original, not high resolution PCM or analog, though most of my SACDs are older recordings that were originally analog.