Keep in mind, that not all MnO2 reacts in this way easily. Strongly calcined MnO2 (very fine crystalline stuff) hardly dissolves and even in concentrated acids it hardly is capable to react. This is a problem with many oxides. When they are calcined and become crystalline, then they dissolve with great difficulty.
Freshly precipitated amorphous MnO2 indeed quickly dissolves in an acidified solution of H2O2, forming colorless Mn(2+) ions.