The nanorods introduced into (RE)BCO thin films are the c-axis-correlated pinning centers, and in magnetic-field-angle dependent critical current density Jc curves large Jc(θ) peaks appear at H//c at high temperatures such as 77 K, where θ is the angle between applied magnetic field and the c-axis. In contrast, the Jc(θ) peaks at H//c become less prominent at temperatures less than approximately 30 K and disappear at 4.2 K. The collapse of the Jc(θ) peaks has thus far been attributed to pinning by small point defects, which is effective only at low temperatures. However, this explanation seems to contradict the recently observed good correlations between Jc values at 77 K, 3 T (H//c) and the in-field Jc values at low temperatures (20–40 K). In this letter, I explain the origin of the collapse of the Jc(θ) peaks at H//c, based on the intrinsic pinning originating from the layered structure of (RE)BCO. The temperature dependence of Jc(H//c, T) and the calculation of the elementary pinning force fp by the core pinning interactions support this explanation.