Thanks. On that note the Underwater Movement (Non-Naval Units) on pp. 56-57 TW rules should also clarify what it means for the UMU-equipped units to move "like a submarine". My guess that if 'Mechs can do it, then units such as UMU-equipped Battle Armor (TW/TM unit) or SCUBA Troopers (TO unit) can also use UMU MPs to move horizontally while at the bottom level.
Edit: This may require an errata to p. 57 TW (under Underwater MPs) regarding UMU movement at the bottom level (not just TO/BMM), so that UMU movement of units other than 'Mechs is also covered. It should be also clarified if Underwater MPs allow units other than 'Mechs (like UMU equipped BA - fully covered in TW/TM, and SCUBA Troops - covered in p. 341 TO), can do everything else a submarine can do (like move vertically in water, or reaching the surface level, like submarines can per p. 56 TW, but 'UMU equipped 'Mechs can't per p. 295 TO).
Edit: I feel, that since rules for vertical UMU movement were left out, the UMU section on p. 20 BMM should be marked as simplified, and should clearly state, that unlike jumping the 'Mech still needs to pay MPs for turning and changing levels.
Edit 2: The crossed out text above is no longer relevant considering Xotl's edit to his answer.