I have recently started a second vault and got tons of real good stuff in those first few lunchboxes, all the ones I collected afterwards were blues and 500caps so I would say they bump up the legendary thing for the beginning few.
Pure luck. When i figured out that the content of your first few lunchboxes determines the way your vault developes for the next days or weeks, i started and deleted several vaults in a row. While the first 4 received just utter garbage (500 caps, some blue stuff), the 5th and 6th received some really nice items. I went on with those. However, later, i realised, it′s not the weapons, but the legendary dwellers/characters you require for a great headstart. One rare or legendary char with good stats and a good weapon, and he will achieve miracles on exploring right from the start...
I dont have any idea what "RNG" is but all this lunchbox contents is like dice rolling. I had 10 vaults until something decent came up. Now i keep it as the greatest treasure. Still i've never had a legendary dweller, but at the tenth try i got a good rare guy with power aromr and a fatman to blowi up the wastes outside. Try to start new vaults until you get someone with a good gun that can go exploring, and another decent gun that you can keep at home to kill raiders and stuff.
opened 40 pack lunchbox and only got 2 legends. from the beginning i think there is a 'Luck / Chance' settled. i deleted several vaults because i wanted to test out room organizing (i despise tutorial)
Clearly it does work or your girlfriend would have got nothing, so there is nothing to fix, you just got tough rolls, just restart the vault and judge whether you want to continue based on the 1st 4 box's. I have been playing for 90 hours, have opened 30 box's and never had anything except common items and caps, does not make a huge difference as I have a training cycle and will soon have 10 max stats to go out hunting for items.