I think you're misunderstanding something. This has nothing to do with selfishness -- you're only really considering the upside.
The harm/good ratio of screening depends crucially of the false positive/negative ratio vs. the actual prevalence of the condition or disease being screened for. (Plus, obviously the psychological/medical "cost" of a false negative/positive.) I would recommend the talk at [1]. This particular issue is brought up about midway through the video, but I recommend watching the whole thing.
The harm/good ratio of screening depends crucially of the false positive/negative ratio vs. the actual prevalence of the condition or disease being screened for. (Plus, obviously the psychological/medical "cost" of a false negative/positive.) I would recommend the talk at [1]. This particular issue is brought up about midway through the video, but I recommend watching the whole thing.
[1] http://www.ted.com/talks/peter_donnelly_shows_how_stats_fool...