Sounds like bad RNG. It happens at times, but if you're on a different comp from the norm your odds of finding your units barely will go up.
It is worth noting however that if that unit isn't tier 3-5, the difference in chance pretty much doesn't matter. Even in those scenarios the unit pool matters more for unit denial, if there's only 2 or less possible three stars every copy being held hostage or used slashes your chances of finding them. There's 39 copies in tier 1, and 26 copies of tier 2 of each champ.
Even assuming 3 people are running the same units, all 3 can 3 star that unit with 12 copies left for another 3 star or two of them can 3 star with the other just barely not being able to three star (8 units left for tier 2) which once players start to die, they'll likely find. Most players only need a 2 star unit for each piece of their comp to be powerful enough to fight. Which means you only need 7% of what's in the tier 1 pool or 11.5% of what's in the tier 2 pool.
Now granted, if you aren't competing with these pools there are more units up. But there's 13 tier 1 champions IIRC. That means the entire tier 1 pool is 507 units, 468 being the wrong unit if you want one specific option. Even if everyone else is running Assassins, it doesn't matter if everyone got 3 Kha'Zix. 486 tier 1s are still in the pool and only 39 are what you need, 447 are the wrong ones. Essentially, assuming everyone got a single tier 1 two star they needed, that takes your chances from 7.7% (1/13) to 8% (39/486). That's right, the entire player pool boosted your odds by a measly .3%.
With tier 2 its not much better. There's still 13 champions, so the math is similar. But the unit pools are smaller so the boost should be more significant. So lets say everyone takes a tier 2 you won't take to 2 star. That means out of a total pool of 338 (26 per type) units, a total of 21 are taken leaving 317. So your initial odds of getting the specific unit are 7.7% (1/13) and the odds after removals are 8.2% (26/338).
As you can see, the boost only went up by 0.2% in a unit pool that has almost 200 less units. The amount of units in the pool is very significant at most levels and most things you will roll will be the wrong unit, that's why you have 5 slots and that's why you need to have versatile game plans when possible. Hell doing this math again at tier 5, you have 10 of each unit in the pool. There's 8 champions in this tier. That means you're trying to roll 10/80 for each champion, or a 12.5% chance. If somehow 7 players last to this level and take 3 of a different legendary, there's 21 removed. That 12.5% chance becomes a 17% chance (10/59). The largest increase not sharing a type will get you is 4.5%, and its in a very fringe scenario.
TL;DR - Not sharing a comp with others isn't an effective means of getting what you want. It's effectively a 0.3%-4.5% increase to your odds.
