Some people swear that without lots of protein, they don't make as much progress in their training, and it's possible that some people truly do benefit in taking in larger amounts per day.
300g is probably more than his body will be able to really make full use of (he'd most likely get the same results with keeping intake at around 1g per lb. of bodyweight he is currently at, around 200g/day), but it is possible that he does get better results in building lean mass with a high protein intake.
But, as there's no formula that dictates how much protein is utilized at most by all people (since protein quality, genetics, type/duration/frequency of training, etc. will all affect this differently from person to person), it would be pretty well impossible to be able to actually 'prove' that his notions of what he thinks he needs for protein intake would be excessive.
Rather, I'd suggest making the point that QUALITY protein sources from plant-based foods can do equally well (pea/hemp/brown rice protein, etc.) in place of animal protein sources, and that when you eat quality food sources, many find that they don't need the same excessive amounts of nutrients they were getting from taking in large quantities of lesser quality, heavily processed foods. In which case, you could certainly "challenge" him to change to trying 200g of protein per day from good vegan sources and tell him you bet that he'll get exceptional results AND feel better for it, too