Always a tricky one, and this is (IMHO) wherecommercial PQQ Schemes add value to the tender process.
(Safety Schemes in Procurement, CHAS, etc.)
These schemes all have set criteria and work on a PASS/FAIL system (but obviously allow for resubmission and reassessment).
Weighting systems are always difficult, being prone to subjective analysis and often wide open to challenge by the unsuccessful contractor. Things become even more difficult if you work in the public sector!
For any question you set, you should really know the answer you seek. Ideally, you should express this in guidance issued with your tender.
My first PQQ question would be to ask them to identify which schemes they may already have been passed/approved/accredited by. Demonstrating that should mean they don't have to go through your q-set at all.
I agree with your Managers. Exclusion purely on the basis of having been served a Notice is IMHO far too strict. A great many reputable Organisations have attracted enforcement attention. Many may have been prosecuted in the past for H&S breaches. There but for the Grace of God etc.
What is really important is how they reacted to that enforcement action, learning lessons and implementing improvements etc.
Perhaps your Organisation may wish to consider joining in SSIP etc as a client /subscriber?