I suspect the avenue to answering this revolves much more around his condition and his reaction to it than it does around statistics as a field. For one thing "legal blindness" is a pretty different thing than complete blindness. I also admit to ignorance of "computer induced medical problems" syndrome (for example how well is it understood, how much does it vary, etc.--just having a wikilink is not like Euclidean certainty.) Also, of course there have been completely blind people who still made contributions in science/methods. Bottom line is I would get some more second opinions (including having him examined) as well as checking out some forums or the like for the blind community. As well as just working with him and seeing how he does.
On a simpler level, I do think working in statistics involves a significant amount of reading, writing (typing nowadays), and coding. If he has a hard time with those activities, it may hold him back. For example (statistic of one), I had a (since recovered) low brain blood flow several years ago and found that it interfered with detail work. Still pretty bright, could converse, even do PPT and Excel in a business setting. But Word footnotes (never an issue previously) were extremely hard on me. Something about detailed reading was trickier for me.
So I really think attention to him and trial of different activities is the key. More so than theoretical ideas of what is required for statistics.
On a practical level, if it's something you/he want to do, I would not let the first contrary answer* turn you off. At the same time, from a Bayesian standpoint, it's not promising that the first answer was negative. And we don't know how much of an examination they did, etc. So...good look into it some more, since...why not? But don't assume that the initial advice was invalid either. Just check some more.
*Rereading, I see it is 5 people that you talked to, not just 1. That doesn't sound good. Still, if it's something you want to do, maybe check in with some other people, such as a neurologist or psychologist who specializes in treatment of the blind. I guess also talking to someone in the blind community (or an occupational therapist) might be helpful as well. For example, an avenue to explore would be how well can Braille substitute for computer text, especially in the work of an applied field. (I don't know, would check to learn.)