Your first example is not inherently true, but we do follow that approach in our weak dor.
We do check the lungs on a shected animal. It depends on how common issur is.
Vegetables, for example, depend on the min, locale, and season as to whether they require checking or not.
The pure rule l’halachah is kol hamarbeh livdok harei zeh m’shubach, but practically, it’s sometimes not advised.