The claim you're responding to is not that they won't allow it to influence their decisions, but that they will actively refuse to even consider a product if they learned about it through an ad.
Most of the ads I encounter are through podcasts because I don't watch TV and ad blockers of various kinds apply everywhere else. I will never use or recommend Squarespace for any purpose, simply on principle.
The current ecosystem is overly focused on manipulation and there are simply to many ads, yes, but I have found really good products via ads and I don't think companies should be generally demonized just for playing the game. It's not all bad.
That's where we disagree. Imagine you always cooked your noodles in a pan. This is clearly a suboptimal situation. Then you see an ad for a pot, you go buy it and it turns out that making noodles (and other dishes) could be so much easier!
Sure, you would not have bought a pot otherwise, but this ad would have been a net positive for you and the ad company, no downsides.
Or maybe you see an ad for a Chinese restaurant, so you try it and it turns out you really like them. There's nothing inherently wrong with their food just because you got to know it via an ad.
As stated above, the current system is stupid. But it's not all bad.
How frequently must these people be buying things for this to even be noticeable.
If I think about regular day to day purchases, I'm not sure how influence plays a part at all. There is no branding or advertising for fruit/vegetables/meat from the local store. Even with household goods, I don't speak the local language so brand names are not easily noticeable.
Maybe bigger purchases? But those are rarer and usually involve some kind of research. I'll happily buy from brands I have never heard of if they show good results in independent tests. It just never feels accurate when people tell me I'm being subconsciously manipulated by ads when I see so few and buy so little.
https://hbr.org/2013/03/did-ebay-just-prove-that-paid
https://www.forbes.com/sites/augustinefou/2021/01/02/when-bi...
I wish I had saved the link, but I read a study that showed people consistently underestimated how likely they were to buy a product after seeing an ad. They would buy it at much higher rates than the control group yet still assert that they were aware of the ad and not allowing it to influence their decisions.