Any certification or certification program is only as strong as the integrity of the people that stands behind it.
The "certification" is a signed statement that the welder in question took a test, followed the rules, and passed the test on a specific day when the stars were in the proper alignment. It offers no assurance the welder will deposit a good weld every time he or she strikes an arc.
The plain fact is that the employer is responsible for quality control. As such, the employer is responsible for the work performed by the employees that work for him. It is a responsibility that cannot be delegated or absolved. As such, it is in the employer's best interest to take the steps necessary to ensure the welder's skill are up to par before putting that welder to work. While accepting qualifications of a previous employer might save some time and money, it is a fools game in the long run. The cost of removing an unacceptable weld and rewelding a connection can cost several times what it would have cost to qualify the welder before putting him to work.
Laboratories and other organizations that qualify welders do just that, they test welders in accordance with specific welding standards, but one must consider the human element. The welder taking the test is a variable subject to all sorts of external influences, as is the individual administering the test. The welder qualification test is a demonstration the welder has the minimum skills necessary to deposit a sound weld under ideal conditions. That being the case, I would rather test the welder under conditions that replicate job conditions, that is, have the welder take the test using the equipment that is used on the job. If the contractor's equipment is in bad repair, it represents what the welder will be using on the job, it is what the welder should use to take the qualification test. If the contractor has no electrode oven and does not store low hydrogen electrodes properly, that's what the welder should use for the test. If the contractor is using XYZ's brand of flux core electrode because it is less expensive (but harder to use), it should be what the welder uses to take the qualification test. The bottom line is there is more involved in producing acceptable welds than simply the welder's skill. The welder qualification test should reflect what the welder will encounter on the project or in production. Taking the welder qualification test under ideal laboratory conditions, using a machine in perfect working order, with a "high quality" electrode does little to assess the welder's ability to produce acceptable welds under actual job conditions.
Best regards - Al