The radial acceleration relation (RAR) shows a strong correlation between two accelerations associated with galaxy rotation curves. The relation between these accelerations is given by a non-linear function that depends on an acceleration scale a_+_. Some have interpreted this as an evidence for a gravity model, such as modified Newtonian dynamics (MOND), which posits a fundamental acceleration scale a_0_ common to all the galaxies. However, it was later shown, using Bayesian inference, that this seems not to be the case: the a_0_ credible intervals for individual galaxies were not found to be compatible among themselves. A test like the latter is a fundamental test for MOND as a theory for gravity, since it directly evaluates its basic assumption and this using the data that most favour MOND: galaxy rotation curves. Here we improve upon the previous analyses by introducing a more robust method to assess the compatibility between the credible intervals, in particular without Gaussian approximations. We directly estimate, using a Monte Carlo simulation, that the existence of a fundamental acceleration is incompatible with the data at more than 5{sigma}. We also consider quality cuts in order to show that our results are robust against outliers. In conclusion, the new analysis further supports the claim that the acceleration scale found in the RAR is an emergent quantity.