Why does a clearance for the approach permit you to descend to the MSA? (i.e. what's the regulatory/ICAO reference for that?)
It may not. My initial research seems to indicate that in a non-radar environment, when cleared for the approach, you would maintain the last assigned altitude until on a published segment of the approach though I would argue that practically, if within 25 sm and cleared for the approach via LZR, you aren't going to hit anything if you descend to 3500' until LZR.
Now if you are cleared via the STAR, you would HAVE TO maintain the published STAR altitudes until on a published section of the approach.