Stable glasses are formed during physical vapor deposition (PVD), through the surface-mediated equilibration process. Understanding surface relaxation dynamics is important in understanding the details of this process. Direct measurements of the surface relaxation times in molecular glass systems are challenging. As such, surface diffusion measurements have been used in the past as a proxy for the surface relaxation process. In this study, we show that the absence of enhanced surface diffusion is not a reliable predictor of reduced ability to produce stable glasses. To demonstrate, we have prepared stable glasses (SGs) from two structurally similar organic molecules, 1,3-bis(1-naphthyl)-5-(2-naphthyl)benzene (TNB) and 9-(3,5-di(naphthalen-1-yl)phenyl)anthracene (alpha,alpha-A), with similar density increase and improved kinetic stability as compared to their liquid-quenched (LQ) counterparts. The surface diffusion values of these glasses were measured both in the LQ and SG states below their glass transition temperatures (T(g)s) using gold nanorod probes. While TNB shows enhanced surface diffusion in both SG and LQ states, no significant surface T-g diffusion is observed on the surface of alpha,alpha-A within our experimental time scales. However, isothermal dewetting experiments on ultrathin films of both molecules below T-g indicate the existence of enhanced dynamics in ultrathin films for both molecules, indirectly showing the existence of an enhanced mobile surface layer. Both films produce stable glasses, which is another indication for the existence of the mobile surface layer. Our results suggest that lateral surface diffusion may not be a good proxy for enhanced surface relaxation dynamics required to produce stable glasses, and thus, other types of measurements to directly probe the surface relaxation times may be necessary.