Asymptotically, sure, you're right. Constant factors are often important in practice, and simple cost models (e.g. ones that don't model cache locality) will no longer give you a decent estimate of constant-factor differences in performance between algorithms.
I think the issue here is that, in the past, with shallower cache hierarchies, models that assumed a constant cost per memory access would maybe be off by smallish factor (I don't know, maybe 50%).
However, now memory access is frequently the limiting factor for an algorithm, and there can easily be an order of magnitude in variation between the average memory access latency for different algorithms (i.e. cache-smart versus cache-dumb).
Really, if you doubt that the RASP model is appropriate for modern architectures, you can test it (a typical exercise in an algorithms course) -- see if, as the input size grows, the timing follows the asymptotic analysis. That is basically what the article you linked to does, and the results are not all that surprising -- where things are linear time in theory, they are linear time in practice; where they are quadratic time in theory, they are quadratic time in practice. It is worth pointing out that in all but the last example, the list and vector operations had the same complexity (because of the linear search), so it was really a comparison between constant factors.