The Pearcey process is a universal point process in random matrix theory and depends on a parameter rho is an element of Double-struck capital R. Let N(x) be the random variable that counts the number of points in this process that fall in the interval [-x,x]. In this note, we establish the following global rigidity upper bound: lim(s ->infinity)P(sup(x>s)vertical bar N(x) - (3 root 3/4 pi x(4/3) - root 3 rho/2 pi x(2/3)/log x vertical bar <= 4 root 2/3 pi + epsilon = 1, where epsilon > 0 is arbitrary. We also obtain a similar upper bound for the maximum deviation of the points, and a central limit theorem for the individual fluctuations. The proof is short and combines a recent result of Dai, Xu and Zhang with another result of Charlier and Claeys.