I agree it's silly, unhelpful advice - and likely to be counterproductive because then you're just feeling guilty that you're feeling stressed which is more stress FFS!
Stress is unlikely to have a significant effect on biology. We know it affects it a bit but it's not likely to make huge difference either way. It certainly isn't going to cause a fertility issue where there isn't one, and relaxing isn't going to fix a biological issue.
But, I do think that TTC can be a very stressful experience if you're expecting it to happen straight away, seeing every negative test as some kind of sign of failure, testing so early that you're likely to see negatives (especially if that's compounded by the above). What can help is reframing experiences - expect it to take up to about 8 months for a start, and try (I know!!) not to test too early, although some people do get positives at 11dpo, it's quite unlikely. 13dpo is really the earliest that you should be testing, but a negative is more likely (4x more likely!) than a positive every month even if you're doing everything right! So having that realistic expectation can really help.
Something that I found helpful was saying that I wouldn't test early unless I had an actual reason to, so if I wanted to drink I'd test, if I thought there were multiple symptoms I'd test, I tested early once because my mum was visiting and I wanted to tell her in person if it was positive. But other than this I tried not to.
It can also help to have little treats lined up for every month that you're not pregnant, that you'd have to cancel if you were pregnant, like something involving alcohol, fairground, hot tub, forbidden pregnancy foods, whatever. That way you have something good happening either way and it's not just crushing disappointment every time.