I'm guessing from a purely insurance perspective that may be the case, but under PSSR anything exceeding 150bar litres (operating Px in bar X Vessel volume) requires a Written Scheme of Examination (WSE) and it will be that Written Scheme of Examination which will specify the inspection frequency and method.Interestingly they are now designed to be tested every year and many insurers do this irrespective of other legislation, they are generally classified (by insurers) as domestic which don't need testing as they won't last that long; or industrial and each insurer has their own requirements. Many never test anything industrial under 5 years old and regularly test anything over 15 years old, and they use different tests.
Anyone operating a qualifying vessel without a WSE and inspection schedule will be in breach of PSSR and as such I'd guess your insurance will have a pretty good reason not to pay out.