Do cd's store a more exact copy of sound than LP's

I am very interested in moving into the vinyl/analog world after several very rewarding auditions. However, I came across this comment of someone in the recording industry:

"LPs can and do sound absolutely sutnning with the right turntable and vinyl, but don't fool yourself - it is a euphonic coloration. SACD, DVD-A, CD or analog tape are a more accurate method of storing a more exact copy of what is on the master tape"

This seemed contrary to my understanding. For example, I understood that CD's recorded at 16/44.1 created phase errors which needed to be corrected by very complicated algorithms. What do the vinyl guru's reply?