I think asking if stressed owners can be a factor in a pet becoming unwell is a bit different to asking if their stress can exasperate a stress-induced medical condition in their pet..
Cystitis is so common in cats, and cats are commonly highly strung by changes. There's so much that would stress one out and not the other- which would also apply if they had a stressed owner.. Some cats may become stressed if their stressed owners actions are something that triggers them I.e being overly cautious with grooming them, clipping nails or bathing. But then, if your animal has a condition that is stress related, any owner should be aware of NOT stressing them out.. But this may not always ring home with some people, and on that hand- yes, owners could be unknowingly making their pets health worse by simply being over cautious.
To others, a pets health may SEEM worse because of their owners anxiety i.e you go to the vet because your animal has an ongoing issue that your vet can't diagnose and it's really affecting their quality of life- when ultimately, it's the fact your vet can't give you an answer and it's affecting YOU which makes you persist and potentially create a bigger problem by over treating them to make yourself feel better.
I think it's something you may struggle to get clear responses from as they will either be from more relaxed pet owners who don't pick up on slight health changes but have always provided adequate care and encountered few problems (this could be argued from both sides and as one thinks their pet had a healthy life until the end, others may think the end shouldn't have happened should they have been more cautious).. Or your other responses will be from Anxious owners who either genuinely have unwell pets, or pets that undergo regular veterinary treatment for issues that may or may not need treating.... But who, as an outsider, can differentiate between that ?
Personally, I am a worrier. I have 2 young sows with zero health issues, one elderly sow with 2 ongoing interrelated health issues and another more elderly sow with several problems.
Do I pick up on the slightest changes with all of my girls? Yes. Would I react quicker if it where my elderly sows that encountered a problem? Yes, because it could have much larger implications if I don't react due their age and ongoing health problems. Would I accept antibiotics from a vet within 24 hours of my pig being "sniffly"? In my elderly sow with heart peoblems- yes, because she is at high risk of URI's.. In my youngsters, I would give more time granted all other aspects of their health and development where normal.
As an anxious owner with 2 unwell pigs out of 4, one with extremely complex needs- I find it hard to give a clear answer to the question. Some may deem me as over treating one but under treating another- Fudge has caused me a lot of worry over the past 20 months, and required a lot of care and veterinary treatment. I am extremely cautious with her- if I wasn't, fudge would have died long ago. Personally, I don't think my anxiety over her health has caused HER any adverse problems- she is a pig that has such zest for life, she is a happy girl. Without my worry and cautious care with her, she wouldn't be ruling the roost right now, she wouldn't be here at all. But I'm not the same with my youngsters, they are healthy and cared for but don't have the same complex issues as fudge- things My vet would treat fudge for WOULD be over treating in my youngsters as they just don't have the same requirements- only I understand fully the needs of my pets and ensure that their wellbeing and quality of life is of utmost priority at all times.. But that's my judgement, as an "anxious owner".
Other than Obvious neglect of a pets needs or causing suffering by over treating an animal AGAINST veterinary advice.. I don't think anyone will ever be able to clearly say another owners actions or health of their pet is a direct result of their anxiety levels.