That's likely mostly true. I don't think having an 'arm day' is a good idea for a beginner in the first place. I think beginners who have arm days end up with shitty physiques. So yea, I think his programming in general probably needs a good bit of work. I think a proper program would have him getting plenty of bicep work via rows, pullups/pulldowns, etc. Enough that direct arm work at the end of a training session could be of some benefit but not absolutely necessary.
I realized I never addressed how I do my direct arm work, so I'll go ahead and do that now. I'll generally just pick one exercise, which could be barbell curls, db curls, or cable curls, and I'll do something in the 10-20 rep range for 3-5 sets. Just depends on how much time I have and how I feel. My time is VERY limited, so I have to be very conscious of training economy. But generally I'll decide my bicep work is done when my reps have decreased significantly at my working weight. Meaning, if my first set was 20 reps, and my 3rd set was 10, and that was a struggle, it's time to stop.
Alternatively, 1 set of 100 reps (or however many you can get through) with an empty axle bar (generally 30-35 lbs) will make your arms grow. Do that a couple or 3 times per week, with no additional bicep work, and watch your arms grow.