All-dielectric nanophotonics has become one of the most active fields in modern optics, largely due to the possibility to control electric and magnetic light at the nanoscale. In this rapidly evolving scenario, artificial Huygens sources have established new paradigms in flat optics, bringing devices closer to efficient wavefront shaping with phase engineering at the subdiffractive level. However, their performance is fundamentally limited by electromagnetic coupling between the constituents of the metalattice. Here, we challenge this well-conceived notion and propose an alternative concept to achieve phase control and full transmission in metasurfaces, based on the nonradiating sources known as Hybrid Anapoles (HAs). Our theoretical analysis demonstrates that HAs are characterized by a negligible coupling. Therefore, in contrast to Huygens particles, HAs can operate as individual meta-atoms even in highly compact designs, are robust against disorder and preserve their characteristics on dielectric substrates. Remarkably, the transmitted wave phase can be modulated with negligible reflection. To illustrate the capabilities of our platform, we utilize a disordered HA array to modulate the phase of an ultrafast gaussian pulse. Our study represents a departure from the established designs and opens an avenue towards the realization of new devices for flat optics with unprecedented efficiency.