Well false, and covered.
Firstly no, nuclear plants do not require daily maintenance. In fact the core / steam loops are largely maintenance free outside of planned shutdowns years in advance. Maintenance is usually only carried out every 24 months.
As to how, it's not exactly rocket surgery. This proposal just lowers two components to the bottom of a hole in a water column, just shut it down, cool it off (like you would do with a normal one), and then all you've got is the extra hour or so it takes to winch the thing up to the surface. It's not in any way buried or sealed down there.
I'm not talking maintenance of the actual reactor. I'm talking dials, valves, switches, even light bulbs, sensors, data collectors, etc. etc. And yes, that kind of stuff is on the daily "to fix" list. These are big complicated machines. You don't drop it in the ground and forget about it. They said they were going to run them remotely, which is really what I call shenanigans. Sure, you can put a couple of PCs anywhere in the world and "remotely control" any reactor, but you need access to all the piping, wiring, etc. and that means a big crew down under the ground.with the reactor.
I think all the maintenance-required parts you're talking about are where the heat is transformed into electricity, plus the safety-related monitoring of the core. With this design, it seems like all of the turbines, etc. will be at the surface, where they can be easily maintained, while the safety-related stuff just isn't an issue. Rather than designing a core that can be controlled and ramped up and down, with this system you'd designed the core to just operate at a continuous steady state for its operational lifetime until the fuel is used up, at which point you just fill in the hole.
You might make the core self-moderating so that if it gets too hot it will ramp down the fission so you don't have to worry about stoppage in the flow of water resulting in a meltdown or similar, but that would only be to reduced the likelihood of the core damaging itself before the end of its useful lifetime, not because there is any safety concern with a meltdown that occurs kilometers underground.