I disagree with that. You need *some* kind of DMM. But I think the cheapest one you can find that has continuity test (preferably with a buzzer) is very useful. Just the other day I bought a $2 pack of five leads with alligator clips. I used a couple of them to hook my breadboard to a 3.5mm jack. I was puzzled why it wasn't working very well until I found that one of the leads didn't actually have continuity between the clips!
Let me try to clarify what I was saying:
With the arduino kit he was looking at, his first few projects are going to consist of installing the arduino IDE, Hooking the arduino up with a usb cable, blinking a led, learning about I/O. And so on. I know quite a few people who do arduino projects and they seem to rarely if ever use a DMM.
For a large part, he's going to be dealing with *computer programming* and basic hookup type stuff and not much actual electronic design at least initially. He's going to know pretty quickly if this agrees with him. And before he needs to buy a DMM.
My recommendation was this: Buy the arduino starter kit. Work through the first few exercises. And then the *second* purchase should be a DMM. And fairly quickly if this agrees with him. But he shouldn't need a DMM to get started and at least get a feel for whether or not this is interesting to him.
When he finally needs a DMM, chances are the cheapest crap DMM he could buy would be good for quite a while - "Is there continuity here", "Is the voltage near 5V", "is this a 10K resistor". Your recommendation of a cheap $10 DMM off of alibaba is not unreasonable. Or, he could invest a bit in the future and buy something nicer and more accurate.
One other DMM note which one might consider is that there is something to be said for just having a general purpose DMM around the house to check plug voltages, etc.. In which case any DMM recommendation I would make would likely focus on safety when measuring the mains and not something cheap to be used only for low voltage electronics. Any reasonable "electrician" meter should be sufficient for starting out electronics.