It's worth always keeping this in mind, and not just taking extra worried people to the gp, but also giving unwarranted peace of mind to those who have a problem.
Even just having them get in a car and go to their GP, or increase their stress levels, have the potential to cause harm. It may be an exceedingly low risk, but applied to a large enough number of people and it starts adding up. When applied to conditions that not everyone has, this can easily tilt the balance.
Consider a hypothetical condition and a population of 1000000. If 1% has the condition at any one time, and the accuracy of the test is 97%, then 10,000 should have the condition. Of those we'd expect 9,700 to get the correct diagnosis; 300 would remain undiagnosed; But 3% of those who don't have the condition - an additional 29,700 - will be wrongly diagnosed.
Let's say this is a condition where 10% would die untreated without this new intervention, it'd be tempting to suggest we've saved 970 people. But early detection might not make that much of a difference - for many things the most severe cases will be noticed anyway and/or late detection is still sufficient to save the patient.
Let's assume for this hypothetical condition, earlier detection will save 10% more of those. In the above that'd save 97 people. Awesome. But lets say it causes 10% more of the undiagnosed ones to die because they wait longer. That's 3 more dead. So net 94?
But if only 0.33% of those wrongfully diagnosed end up dying as the result of the misdiagnosis, be it car crashes on the way to the GP, or the visit leading to a follow up error leading to an intervention that is generally but not always safe, then the wrongful diagnosis would kill 98 people.
I'm not saying that would be the case here. But it's an illustration of why it is important to consider not how many problems are detected, but what benefits early detection gives vs. the cost of wrongly diagnosing people, even when it seems benign enough (just another test, and they'll confirm it was a mistake?)
E.g. there's been pushback against large scale breast cancer screening for this very reason: They're very successful at finding cancer early, but most gets found eventually anyway, and the improvement in long term survival rates from the earlier detection is reasonably small.
Couple this with low overall rates of occurrence across the total population at any given point in time (cancer rates look high when considering "will X get cancer at some point in their life?", but most people will be free of cancer at any given single point in their life; even most people who have had cancer), and the impact of false positives and potential health implications of a (very small but still existent) risk involved in even something "simple" like a biopsy, and it's unclear if large scale screening is ethical (over general populations; screening of groups with sufficiently high risk factors is another matter entirely).