I've never heard that it matters at all. I don't think they'd even necessarily know?
I suppose if you got a scholarship that was prestigious, that might count.
The issue with non-funded degrees is, if you work alongside (which most people do even if they're funded), you might take longer. This lad who is sueing, he could take a year or two out, work, and get up the money that way.
But once you've taken longer, you're no longer eligible for some of the jobs going. Most Oxbridge junior research posts want you to have completed your masters and PhD in a certain time limit, and some specify you must have no fewer than, say, five years between graduating from your undergrad and getting a PhD. They'll accept exceptional circumstances at discretion, but basically, you have to make your case if you're a mature student or you've had years out to earn some money.
I know this student is only just starting a master's so this may seem as if it's not really important (he might perfectly well go on to do something non-academic), but I think it's crucial because the people who make these rules about time limits are the same people who are insisting that this student should have 13k. They must know what they're doing, and that it'll end up as self-reinforcing discrimination, because they will end up with dons who've been the students who could afford it all.