Strictly Speaking, Yes... But
There is nothing in the PHB that indicates to me that any of these are optional. As always, the GM can always choose to ignore or modify certain rules as they see fit (as noted in an answer above) but it's important to understand the reason for the rules and the possible drawbacks to them.
Uses for these things:
The first use for these things is given right in the PHB: It is a tool to help the players flesh their characters out and make them coherent and consistent.
Another use, also mentioned in an answer above, is to help the GM design encounters around player characteristics: "How do I motivate these guys... aha! Bjorn is prideful and wrathful, and Sonja has it in for the merchants guild of Qithay, so if one of them insults Bjorn that should hook them!"
And a final use is to help the players coordinate amongst themselves during character creation if they so wish or if their GM nudges them on that path. I have found this extremely useful for getting PC groups that at least have some reason to be travelling together and who are not completely antagonistic to each other.
There are possible drawbacks, though. There are a lot of ways to categorize players, but one way is "Develop at start" and "Develop in play," which are basically what they sound like. Some players really like to front load character development like this and do it up front. If they put a younger sibling in their background, you can ignore it for 15 sessions, and then when the sibling shows up, they will remember and act accordingly. (They might even have complained, "Hey, where is my little brother in all this?")
Others are the opposite. They can go through the motions, but it takes some time before things gel, and there is just no guarantee that they will gel with what they actually wrote down. By the 15th session they may have forgotten their character has a sibling, or find that they can't summon up the right response. And so they might have trouble coming up with anything at all, or might push back against the whole exercise.
These are dramatic examples, of course, but they get at real-life behavior. I tend to be one of the former and it took a long time and multiple descriptions to really get it through my thick skull that the second type of player exists.
Now, based on your players' statements (they already knew their characters) I don't think this applies. My response would have been, "Great, I want to know your characters, too. Write it down for me, yes?" But it is useful to remember that not all players find these tools helpful.
Unfortunately, I do not have a quick, easy, or reliable way of telling what type of players I'm dealing with, except through lengthy observation.