Aw, man. This topic has been beatin' to death on this forum.
Under most circumstances, tests and books are going to encourage you to administer high flow oxygen. Some tests, like if you take an ACLS or ITLS class, will probably encourage you to titrate it to an FiO2 of 94 or higher.
I highly doubt that the problem with oxygen is a decrease heart rate. If the heart rate is decreasing because of the oxygen then that probably meant that they needed the oxygen. Tachycardia can be a sign of hypoxia and you could expect the heart rate to go down if the hypoxia is treated. The problem I have read with oxygen administration is that it increases
reperfusion injury due to it being a free radical. I think this is mainly an issue with myocardial infarctions and ischemic strokes. I guess it can be harmful to newborn causing damage to the eyes. I am not sure if this is because of free radicals or because oxygen is a very mild arteriole constrictor and this constriction is blocking blood flow to the eye. For most other types of emergencies, I don't think it is significantly beneficial or harmful to give.
Like Teedubbyaw said, SpO2 is only one piece. The patient could be compensating maintaining a normal SpO2 even though they need oxygen. If you put a pulse oximeter on your finger, hold your breath for as long as you can, you'll see that your heart rate will elevate and you will probably feel the need to take a breath before your SpO2 even drops. Instructors like to bring up carbonmonoxide poisoning too. These patients will probably be at or near 100% SpO2, but their hemoglobins will not be saturated with oxygen. They will require high flow oxygen to displace the carbonmonoxide. These patients should not be denied oxygen even though their SpO2 is normal.
Denying a patient oxygen to a patient that needs oxygen is more rapidly deadly and harmful than giving oxygen to a patient that doesn't need it. If in doubt, give oxygen. Typically low flow with a nasal cannula is good enough.