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RNG is determines what determines the result of anything left to chance. Legendary items are very rare, about 3% drop chance from their designated source on TVHM if I remember correctly.
While UVHM boosts the odds, even at 5% from a designated source, you'd assume around 20+ runs for 1. On top of that, LLMs aren't Designated Sources for *anything* that I know of, unless they are for the Relics. LLMs simply have a very large loot pool they can draw from, and drop several item drops(not ammo or currency) that can come up Legendary or Pearlescent.
tl;dr: This isn't unusual at all. Annoying, but not unusual.
Assuming that you're referring to the Ancients relics, those are only dropped by LLM's (ie. only in UVHM). Still, I suppose 0% could be considered "a tiny chance". :-)
I only play solo, but I'm sure that having someone that's a lower level playing with you has no effect on LLM drops. If it did, it probably would have come up in the Gearbox forums (those people are always analyzing things :-), and I've never seen anyone even suggest that possibility.