As for your question, yes, one needs to choose the op amp carefully. Op amp manufacturers show in their datasheets the gain and phase bode plots as well as the phase margin versus frequency. Typically, if you choose a unity gain stable op amp it has less chances to oscillate below unity gain. However, as manufacturers try to boost the gain as much as possible, due to competition, the op amp internal compensation may be just about right to make sure the phase margin is above 45 degrees all the way down to 0 dB gain. Below 0 dB gain, one might see an extra pole and that means trouble. Therefore, since there are many op amps out there and the designer circuit might have a capacitor that reduces the bandwidth even more, I can only advise to always check the manufacturer datasheet and the phase margin plot for that particular op amp of choice.