I'll answer this question a couple of different way. Unfortunately, I didn't read all the replies so some of this might tread old water.
Anyone playing D&D should have read the PHB (DM's included). As for DM's, the DMG is pretty much optional and well as the Monster Manual. The reason these two are optional as you don't need them to actually run a game. Now the DMG really loses its value the more years you have played. From edition to edition, a lot of the information is the same (how to build dungeon/encounters). Though it is nice to see how magic items look in a given edition. The DMG is really not required, but is still a good read for experienced DMs. There is a reason this book was produced last of the three. 1st Edition DMG, now that is a different story; it is almost a required tool at the table.
Likewise, the MM isn't really needed either. The MM is just there so you can populate your world without a lot of work creating creatures. By no means is it necessary to play the game. More experienced DMs will use the MM as templates and customize those Monster based on the encounter, the environment, and the campaign. As a reference though, the MM is the most valuable asset beyond the PHB.
Now given that the PHB is required reading to play D&D, a group can play different styles based on the DMs ideas/goals as well as the player's input. I have played very strict rule-oriented games (by-the-book), more casual (look up that rule next session) and totally free-form. Though the free-form games (with very little dice) are usually one-on-one games. And in this case it does make some sense (1st Edition had no ability checks-sans Rogue). There is no need to make ability checks per say--the DM describes a challenge and you attempt to overcome that challenge. If one way does not work you attempt to find another solution. This can be a fun way to play. However, the DM must tread carefully in not making a challenge only passable one-way. It can be easy for this to occur if the 'overlord' wants the obstacle to be mitigated their way. Heck, I have been known to do this from time-to-time, but I quickly remember it is the player's game--not my game. I think your DM might be suffering a bit from this mentality; sometimes it just take a nudge to remind them this is not a novel. If this occurs often, it is a problem.
The last thing I will say, and this is just everyone in general. When joining a new game or group, people should come forth with the expectations and input on all sides of the table. People enjoy very different types of mechanics at play. The DMs job is to find a balance for all those players--if there is a disconnect between the player and DM then perhaps the group isn't the best for either.