Generally, the answer is no. Tests may be relevant at (a) no load, (b) operating load or (c) overload. Particularly relevant to equipment with moving parts and controls, or equipment which has been repaired.

HSE Guidance usually suggests referring to supplier data and recommendations.

I guess strictly speaking your Insurer's specialist engineers will have conducted thorough examinations, not "inspections".

When you say "The company had also had the equipment tested by a competent company" you need to be certain what the nature of that "test" was. Frequently this means no more than periodic maintenance, with no load test (which is often enough).