Hiya!
Suffice it to say this statement only has broad relevance if you play in a hardcore old school style, and there are many playstyles for which this is not relevant at all. Having more information at your disposal is never BAD, but it certainly isn't necessary.
DMG, pg 5, 5th paragraph under "Part 3: Master of Rules". <-- basically says "You're the DM, you need to know the rules or where to find them if you don't".
More info at your disposal is always a good thing, full agreement here.

And, as I said, as you (general "you") DM, you get better and better are really knowning the rules and how they work together. Knowing that
Charm Person makes the victim think of you as "a friendly aquantence" and then knows it was charmed when the spell ends...that is very useful info. Especially if you are coming from an older version where Charm Person could last, literaly, for the life of the creature and that creature would
almost lay down it's life for you...it will lay down it's life for you if it fails another save (thinking back to 1e here). So if you, as DM, are just going with your previous knowledge, and relaying on a player who may be doing the same, well, that's a potential problem as far as BA goes with 5e. Thus,
every DM, not just ones "playing hardcore old school style" need to know all the stuff in the game (or at least where to find it).
No. Just no. I don't run games to be a human reference sheet, and I have too much to do/know in my professional life to feel responsible for memorizing all of the game rules. D&D is a group activity, and the social contract I forge with my players says that they're responsible for knowing their stuff because I don't have time to both create a fun game every week AND learn all of the ins and outs of their characters. Do I pick most of it up? Yes, I do. But when a player uses a class ability, I ask them what it does, and they tell me the important bits, or just do them if it's something that's pretty common. I don't worry about it unless I notice something off (which occasionally happens), and then I ask questions. But, at no point, do I ever consider it my responsibility to know everything about the game.
On the first part...yes, you need to be a human reference sheet if you want to be anything even approaching a great DM. You can get by with relying on players for stuff, sure, but you (general "you", again) will never be a
great DM. This is fine for most groups (hell, probably all groups!), but it doesn't change the fact that a truly superior DM will know the game inside and out. And the real test is, as always,
"Is everyone at the table having a good time?". As long as that answer is
"HELL YA!, then keep on keeping on.

However...
If a DM is getting frustrated because the players are only putting minimal effort into "learning" their characters capabilities, what do you think the players are feeling when the DM doesn't know his? Different side of the coin. If I'm playing in a DM's game, and the DM whips out a monster that has the ability to cast
Disintegrate, and I fail my Dex save, and then the DM says "
You and your gear turn into a pile of smoldering ash!", I'm going to be annoyed. I'll have to point out that it doesn't work that way. I take a LOT of damage...if I'm reduced to 0 or lower hp,
then I'm a steaming pile. Otherwise, I just take a lot of freaking damage. Now, this may cause the DM to go "Oh, uh, ok. I didn't know that. Sorry!" (which may or may not cause me to question the DM's capability to actually DM...if he got this wrong, what about other stuff in the game?)...or it may cause the DM to go "No, I don't run it that way. You're dead." (which is fine, but then I'm asking myself...what other rules, spells and things are 'changed' that I don't know about, and is he just making this up on the spot, or does he actually have a set of home rulings?).
Anyway, I still stand by my earlier post. A DM
should know ALL the rules in the game (including spells, abilities, etc). It's how much of this knowledge that is accumulated that really helps a DM run a superior campaign. Of course, "should know ALL" isn't a requirement for playing in a D&D game and having a good time. Hell, some of the best times I've had playing RPG's is when we don't know anything about a new game and are learning it, fumbling our way around the rules like newborn kittens. But, as time goes on, we learn the rules. The DM/GM/Ref/Whatever needs to step up more and learn more stuff. If he doesn't, he's nothing more than "just another player, rolling dice for the monsters".
Yeah, my Curmudgeoney Grognarditis is flaring up again.

I'm an "old school" DM (...learned to DM back in 1980 and have been learning and improving ever sense...I hope...

). I fully believe that the best campaigns are run by people who really do treat DM'ing as a
hobby and not just as "a game we play every weekend". A superior DM doesn't just "read and do DM stuff on Saturday for a few hours", he reads his rule books, reads stories, explores art styles germane to his chosen milieu, plays other games, and generally seeks out knowledge about everything that may help him present a believable campaign world.
Again, I've rambled on too long. Sorry, I do that.

To sum up: A decent and fun game can be run by a semi-knowledgeable DM, but a superior and fun game requires a fully knowledgeable DM. Basically.
^_^
Paul L. Ming