I'm in line with Scampi and GM. This happens all the time in Small and Very Small companies. I am a quality department of 1 person. I cannot possibly be on site 10 hours a day 5 days a week to follow behind and verify everybody's tasks. We're going to have a problem with BRC internal audits since I cannot own the documents and be the internal auditor.
Back to your Sanitation Supervisor doing the swabs, you can write into your plan/SOP that this task will be verified/audited/observed by a QA person monthly or Quarterly. So at some frequency, a QA person goes with the Sanitation Supervisor and observes them performing the task and compares it back to the SOP for compliance. This ensures the oversight that the training was effective and that the Supervisor is continuing to follow the SOP as trained and intended. Most people can put on a show but if they truly aren't following the SOP everyday then their "bad habits" have a way of slipping out during observation.
All good points and much as you're alluding to, it's down to the business size as for if this is acceptable. In UK Health and Safety law there is a principle of doing things which are "reasonably practicable" so you don't have to do absolute perfect best practice but if it's practicable for your business size and resources, you should. If it's not, that's also acceptable.
I do think as a principle though that if you can segregate duties, you really should. It's not of course as bad as the person doing the cleaning taking their own swabs but it's not far off. But it all depends on risk. If this is a meat slicer we're talking about in a high risk facility, I'd not take the risk. If it's a mincer for raw meat, yeah that'd be fine.
I find it surprising how little attention is given to verification in HACCP, not just in peoples plans but in guidelines for it. It might be half an hour of a week long course or a page or two of things like Guideline 42. Ultimately though, verification is your early warning that things have gone badly wrong, or, even worse, a too late warning depending on what kind of verification activity you've chosen. If you look at FMEA, which HACCP was based on, detectability of failure of the system is baked into the hazard analysis type step. Somehow it's become an afterthought. You would not believe how many sites I've been in to where I'd identify the HACCP plan has essentially already failed because they are receiving significant numbers of consumer complaints relating to something the HACCP plan is meant to control. How many food business operators think about it that way? Zero...
So I'm going to champion putting more effort into verification and, as previously this swabbing was done by the Technical department (so they presumably had the resource which they're now losing), if the reason for this change is saving money, I'm unconvinced it's money I want to save...
But I accept there are situations, businesses etc where this might not be reasonably practicable and proportionate. Only the Op can make a call on that...