Protoplanetary disks are believed to evolve on Myr timescales in a diffusive (viscous) manner as a result of angular momentum transport driven by internal stresses. Here we use a sample of 26 protoplanetary disks resolved by ALMA with measured (dust-based) masses and stellar accretion rates to derive the dimensionless $\alpha$-viscosity values for individual objects, with the goal of constraining the angular momentum transport mechanism. We find that the inferred values of $\alpha$ do not cluster around a single value, but instead have a broad distribution extending from $10-4$ to $0.04$. Moreover, they correlate with neither the global disk parameters (mass, size, surface density) nor the stellar characteristics (mass, luminosity, radius). However, we do find a strong linear correlation between $\alpha$ and the central mass accretion rate $M\dot{}$. This correlation is unlikely to result from the direct physical effect of $M\dot{}$ on disk viscosity on global scales. Instead, we suggest that it is caused by the decoupling of stellar $M\dot{}$ from the global disk characteristics in one of the following ways. (1) The behavior (and range) of $\alpha$ is controlled by a yet unidentified parameter (e.g. ionization fraction, magnetic field strength, or geometry), ultimately driving the variation of $M\dot{}$. (2) The central $M\dot{}$ is decoupled from the global viscous mass accretion rate as a result of an instability or mass accumulation (or loss) in the inner disk. (3) Perhaps the most intriguing possibility is that angular momentum in protoplanetary disks is transported non-viscously, e.g. via magnetohydrodynamic winds or spiral density waves.