Funny, if I'm wrong, that means a lot of military folks I've known also have this down wrong as well. It could be one of those misunderstood parts of military law and I'd rather know exactly what the law indicates.
If it is not covered by the Geneva Convention, then is it covered by the Hague Convention? Sure, open tipped ammo can be used by the military but are ammunition which are actually classified as "hollow point" used by the military? Is there a deliberate reason why other expanding ammo was made in a way that could avoid being labelled as "hollow point"?
Right on the money sir, the Hague Convention it is! It states
"The Contracting Parties agree to abstain from the use of bullets which expand or flatten easily in the human body, such as bullets with a hard envelope which does not entirely cover the core, or is pierced with incisions." At this point it's worth noting that the US was not a party to this accord. The only part that is binding is in Hague Convention of 1907 in which is states
"…it is especially forbidden -To employ arms, projectiles, or material{sic} calculated to cause unnecessary suffering;" The US did sign onto that one. On 12 October 1990 in regards to the use of open tip rounds by US personel the Judge Advocate General relesed this finding in regards to the M118LR ammo (which is the same defense used for the Mk262 ammo)
"The purpose of the 7.62mm "open-tip" MatchKing bullet is to provide maximum accuracy at very long range. … Bullet fragmentation is not a design characteristic, however, nor a purpose for use of the MatchKing by United States Army snipers. Wounds caused by MatchKing ammunition are similar to those caused by a fully jacketed military ball bullet, which is legal under the law of war, when compared at the same ranges and under the same conditions. (The Sierra #2200 BTHP) not only meets, but exceeds, the law of war obligations of the United States for use in combat." If you will note, the BTHP desgnation refers to Boat Tail Hollow Point. So, you may ask, how can a round that is acually sold as a "hollow point" be legal in war? Well, that's for the lawyers to figure out but it damn sure works. You asked me if ammo that is actually labeled hollow point is used by the military... obviously yes, as I already indicated. These rounds are in use every day and I happen to have some M118LR for my M14 EBR-TACOM RI sitting in my wall locker right now. My goal is not to tell you or the lots of other "military folks" that you apparently know that you are wrong, but I hate seeing people throw the Geneva Conventions thing around all the time. The only references are in the Hague Peace Conferences of 1899 and 1907, and even then the wording is extremely loose. Other people can go on beleiving that the Army doesn't use hollow points, and I'll keep right on using my M118LR Boat Tail HOLLOW POINT. Oh, and by the way in 1993 Winchester 230gr JHP (stands for jacketed HOLLOW POINT) was cleared for use by SOCOM in regards to the Mk 23 Mod 0 pistol. These are all in memorandums of law that are available online for viewing, most authored by W. Hays Parks Chief of the JAG's International Law Branch, in case you are interested.
EDIT: (by Hollow point in my earlier post, I meant what the average person on the street thinks is a hollow point, i.e. a gaping hole in the front with a soft core for a rapid mushroom effect.)
One more side note... in 1985 the JAG ruled that the use of hollow point and expanding ammo is authorized for use in counterterrorist actions. The rules against certain types of ammo only cover parties to the Hague Conferences and those subject to the law of land warfare (read: actual armies of actual countries, not terrorists). Hope this helped you understand the issue. I really cannot get any more specific than this without writing a full out essay here. I could find you some links or something if you are still unclear.