Hi Vendeeglobes
I'm not sure the answer to your question is entirely obvious. The altitudes essentially come in two forms, the obstacle clearance altitude (OCA) and the procedure altitude that is displayed on the approach plate (the OCA is also sometimes displayed e.g. look at the RNP approaches to Gloucester EGBJ in the UK AIP). The OCA provides the required clearance over terrain and obstacles whilst the procedure altitude is adjusted to factor in a multitude of factors including minimum length of procedure segments and requirements of other airspace or procedures. Where the OCA and procedure altitude are the same or close then you can expect to see a 'not below' line under the procedure altitude.
Where you are being radar vectored, ATC will be working from a radar vectoring chart and I suspect (but can't at the moment provide references) that may allow a descent below the procedure minima. I'll be interested to see how the discussion progresses.
Cheers
TeeS