Precisely correct, it's mathematically proven (Nyquist-Shannon Sampling) that the CD audio standard captures and reproduces all discernible frequencies that humans can hear. What you put in is exactly what you get out from a storage medium standpoint, with the standard. You're right to state that it's the character people like/enjoy from the vinyl, but it's definitely not more detailed than a CD.
Amidst the ocean of variables (original mixes focusing on audible range/frequencies, better THD ratings on older receivers, speaker designs focused on fidelity and not size, etc.) the whole arguments chalks up to "It depends" from my perspective. I have a lot of vinyl and a working turntable, receiver, and speakers from 1979...but I'll readily admit it's not putting out more detail than a CD played through my Nakamichi CD deck would on the same setup.
How CDs (and audio in general) are mixed today is a different topic entirely, but it's worth noting that it muddies the waters on this topic.
