Edited by user 17 March 2019 10:28:31(UTC)  | Reason: Typo

There can be a mismatch between the screening process and actual site performance, so this is entirely reasonable. 

It is also reasonable for the client to perform unannounced inspections of your work, perform periodic audits and review your documentation.  You may have to conduct joint incident investigations, attend their training courses and adopt certain client BBS programmes and so on.   You need to consider the time/cost/effort required to meet these requirements and price this accordingly.

If there you still doubt certain issues in their T&C's then use the tender clarification process to ask them under what circumstances they could issue improvement / stop work notices.

The key is to build a good relationship, become a trusted partner and get repeat work.

There is a good argument the client is responsible or the health and safety of the project. That said, clients are rarely held accountable for safety violations...but that another story. Meanwhile, it is not unusual for clients to take an interest in safety related matters. Sometimes it can be quite healthy and other times a pain in the rear end. It really does depend who is enforcing safety from the client's team - are they sensible about it, do they have the requisite knowledge to make a judgement, or are they just a jobsworth out to make a name for themselves?