Your theory may be relatively reasonable, but technically incorrect.
When it comes to random number generators, there is something called a seed. A seed value is very important, in that it allows you to make minor changes to a simulation (something that uses a random number generator), and keep the same random values to see the impact that the minor change had on the results.
So, you may have a seed, that pulls the following random numbers from the generator:
0.9999999, .0132, 0.456, 0.35,.....
Now, if I don't change the seed value, the next time I run the simulation, I would get the exact same string of random numbers:
0.9999999, .0132, 0.456, 0.35,.....
So, lets say that the 0.9999999, nets you a Thunderlord. It's the 1st result on your string of random numbers. So, if the 1st result is a loot table that can pull a Thunderlord - you get it. If it's not, then you may not have another random roll that high until really far out in the string of random numbers - which may be outside the length of time you would on the game. If you fire the game up the next day, if the seed doesn't change - you once again lost your great roll.
So, the question is how has Bungie set up their seeding system for characters in the game and how often does it change. If it doesn't change very often, or is cyclical (Seed1 is used on Mondays, Seed2 on Tuesdays, .... Seed7 on Sundays) - you could end up having characters that can't get drops.
EDIT:
So, everyone would have the same loot tables - but everyone would have different seeded random numbers hitting said loot tables. That is why you would get some players with multiples, while others with none.
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