ARURF
STOPPPPP GIIIVVINNGGG MEEEE BARDDD GODDDD DAMMITTTT. ITS NOT RANDOM IF I GET HIM CONSTANTLY
STOPPPPP GIIIVVINNGGG MEEEE BARDDD GODDDD DAMMITTTT. ITS NOT RANDOM IF I GET HIM CONSTANTLY
But Bard is so OP.

You fricken 1 shot people with an auto attack.
On a serious note, I know what you mean. I've gotten Kalista, Tahm, Alitstar, and Twitch like 10 times each. Granted, for some of those people dodge and I get something different next time, but it's still frustrating when you get the same few champions over and over again.
Getting a certain champion over and over again doesn't mean it's not random. Just a run of rotten luck, like all RNG.
Of course, it's not actually random (or even "almost apparently random") due to differences in champ unlocks.
And besides that, there is something in their roll algorithm that sometimes favors a certain kind of team composition. (That's been established in ARAM, by the way. In computing, statistical aberrations on the order of frequently winning the lottery usually have an explanation other than "it just happened randomly that many times in your experiment.")