There's a HUGE difference in auditing the organization - questioning them and seeking evidence of how THEY have determined that their processes and performance results, product conformity etc demonstrates they achieved what they planned to do, and the declaration made in the title.
It occurs to me that the original statement is a legacy from when ISO 9001 didn't require the effectiveness of processes to be measured/monitored against objectives etc. (that's the 87 and 94 version, BTW). There was no "performance" on conformance. We, as CB auditors, were (somewhat) required to determine effectiveness and it was really difficult. Partly because the Brits wrote ISO 9001 and based it on a military standard (Def Stan 05-21/05-24) it didn't include customer perception as something to measure/monitor. It didn't require demonstration of effective process controls. In fact, the meme about making cement lifejackets wasn't far from the truth!
Today, that's not the case. ISO 9001 requires (if we are to conform with those requirements) to demonstrate implementation and effectiveness. It's the Organization's job to demonstrate those NOT the auditor's job to determine. It's simply confirmation/verification.
The mission has changed, yet (some) auditors and also (some) auditor trainers are still back in the 20th century with their understanding - IMHO!