Rebreathers may feature slightly elevated oxygen levels vis-a-vis standard air (you need a lot of knowledge to use one safely, so presumably anyone diving a rebreather has done the far simpler courses for nitrox or trimix, both of which are used for limiting nitrogen narcosis), but for military divers it's much more about the lack of bubbles and noise.
Rebreathers may feature slightly elevated oxygen levels vis-a-vis standard air (you need a lot of knowledge to use one safely, so presumably anyone diving a rebreather has done the far simpler courses for nitrox or trimix, both of which are used for limiting nitrogen narcosis), but for military divers it's much more about the lack of bubbles and noise.