Why are people talking about OOG situations in this thread? You would have been neutral (or close to) before you ran out of air so as soon as you ascend you become positive. No reason to drop any weight in an OOG emergency. This is covered in the basic PADI course and is why we don't get taught to ditch weights during a CESA. If need be then orally inflate your BCD further when you are on the surface.
If people wan't to discuss dropping weights to counter a blown BCD then I can follow the logic but not OOG.
Perhaps I can clarify, given I put OOA my post.
During your OW, you're quite correct in stating what you were taught. It's taught this way to make thing simple and clear, rather than overwhelming the student with options. When you are under training your instructor supports you (although you may not realise this) generally by holding your 1st stage. In a calm situation yes oral inflate rather than weigh drop is one way. Generally people aren't calm though.
The reality is this. If you are at the surface you want to achieve positive buoyancy as quickly as possible. You know from your course that oral inflating your bcd can take 3 or 4 good breaths.
In real life say you surface in a slight swell, say with a malfunctioning power inflator, you may not wish to take your reg out to oral inflate, and chose to ditch weights first. The priority always is to get positively buoyant on the surface first by the quickest way whatever the circumstances. So it doesn't matter whether you oral inflate power inflate or weight drop or combine inflate and weight drop. Always get positively buoyant at the surface by the fastest means
Safe diving