The Marines kept their M1903's until well into 1942 and every effort was made to make sure that all our troops had the right ammunition and clips. (Remember, unit supply officers were responsible for ordering ammo and they should have known what equipment their own men had.)
I can't say there were no SNAFU's but an M1 with no clips was effectively out of action. An '03 magazine could be loaded with loose ammo or ammo from M1 clips or MG belts (removing the latter was not easy!), but the M1 was a single shot rifle without clips.
Clips were not important for users of the M1903A4 since the scope prevented clip loading in any case.
In my experience, EM's war stories began as soon as they left combat and were well rehearsed by the time they got home. Many (most?) were pure BS; every Walther PP had been taken from Goering personally or at least a German Field Marshal, every Arisaka was captured in a bayonet fight with Tojo.
And of course the weapons stories were the same way.
But I did find out that one I disbelieved for a long time may have been (or at least could have been) true! Japanese 7.7 rifle (rimless) ammo not only will fit and fire safely in an M1903 but the Japanese clip will work as well. It will also fit and fire in and function an M1 rifle, but of course the M1 needs its own clip.