PRAM with no bit operations and P vs NC
Without further information, it's hard to tell exactly. However, to the best of my knowledge, bit operations may be intended as follows. Consider the problem of finding the maximum element in an array of $n$ real numbers. This problem can be solved by an EREW algorithm in $\Omega(\lg n)$; moreover, no CREW algorithm can do any better. 

However, this problem can be solved in $O(1)$ time with $n^2$ processors using a common-CRCW algorithm (in this model, when several processors write to the same location, they all write the same value). The key point here is that a CRCW PRAM is capable of performing a boolean AND of $n$ variables in $O(1)$ time with $n$ processors (which allows overcoming the $\Omega(\lg n)$ lower bound). I think that bit operations may refer to this powerful AND capability of a common-CRCW. 

Additional information regarding the FAST-MAX algorithm can be found in the first edition of CLRS Introduction to Algorithms, chapter 30 (ALGORITHMS FOR PARALLEL COMPUTERS).