That depends on the game and the feature of the game that requires the randomness though. True... pure randomness over spawning points for enemies in an action rpg game, might kill the experience. But if I am playing poker.. I do expect something close to pure randomness when you are dealing my cards.
I think people are confusing the term "true random". It's still truly random, but it won't have a uniform distribution over all possible values. For example, a common trick in FPS games is to pick a random spawn point, but exclude spawn points that are too close to other players. Still truly random.
Another trick in RPGs is to increase or decrease the odds of a successful hit according to recent hits and misses, bringing the short-term average much closer to the expected value. It's still "true random", but uses correlation between attacks to create an underdispersed distribution overall. (Basically, you want to make the variance lower to make people happy.)
"Truly random" is usually contrasted with "pseudorandom". In that sense almost all games are not "truly random". But you are right in that "truly random" also doesn't mean "uniform".
Example: My hobby is that I'm a tournament judge for Magic: the Gathering. I also play a bit, because I like the game. And there's an online version... which has a shuffling system that's actually random (i.e., has reportedly been examined by the same folks who certify stuff for casinos, and passed).
But that causes a lot of complaining from players, because real random shuffling is very different from what human beings accomplish when shuffling pieces of cardboard, and is actually a different standard from what's enforced in tournament play (requirement there is that after shuffle, no player is able to know locations, relative orders or patterns within the deck, not that the deck is "random").
At any given time there are thousands of players online, and every deck gets shuffled at least once per game. With those numbers... unlikely results happen. They happen a lot. And they get players really, really angry, to the point that most forums have "complain about the shuffler" permathreads, because those results tend to absolutely screw you over when they happen.
I worked on a strategy game (think Risk) with an element of randomness (dice rolls) and our hardcore players were very very keen on the true quality of our randomness. I wound up persisting the context and result of every single roll cast so people could see summaries per-game, per-turn, per-user.
