The think that is often missed is that ISO 9001 is often called a "quality spec". It is not. It is the requirements for a "Quality Management System". Emphasis on the "Management".
It has nothing to do with holding extra tight tolerances, or extra smooth surface finishes, or nice edge breaks, etc. It has to do with reliably meeting the customer spec, regardless of how "high quality" an item made to those specs would be. If the customer spec is 'Hole 6" +/-1"', then a guy with an O/A torch cutting it free hand is probably good to go. It can be inspected with a tape measure. If the customer spec is 30' long rope, +/-1', then properly laid out and documented scratch lines on the floor may well be fine. If you're making Class X gauge pins, then digital slide calipers of any provenance aren't going to make the cut. Your measuring standards, equipment and processes are required to be able to reliabily identify the difference between conforming and non-conforming product.
Some of the things I've seen that ISO 9001 is trying to defend against:
1) You order some parts to Rev A of a drawing, and you receive conforming parts. There is a design defect found, so you revise the drawing and order Rev B. The parts arrive conforming to Rev B. 6 months later, you put in another order for Rev B parts, but someone at the vendor builds to Rev A, because the vendor can't keep their paperwork straight. They still have Rev A drawings floating around, and staff don't know where to go to ensure they have the correct rev.
2) The quality inspector on day shift inspects a batch of 6 parts and finds one of them defective at the end of the day. Night shift comes in and sees the parts are done, so the shipper packs them up and sends them to the customer. The vendor lacks a known way to mark and segregate non-compliant parts, so the shipper didn't know it was defective.
Any company of size that regularly ships correct part is going to have systems that are equivalent to what is in the ISO 9000 series. Can you ship quality parts without ISO 9000? Of course. Can you have ISO 9000 and ship junk? Of course. But you aren't going to have a large multi-shift operation regularly putting out the right product in tolerance without processes similar to what ISO 9000 requires in place. The least value of ISO 9000 is for the solo business operator that is part of every customer and vendor meeting, reads every customer and vendor email, does all the work, and can remember everything. The more people involved, the more formal the processes and communication need to be.