She's just prematurely trying to make Dr Vee her brand. I won't be bitter and say that being accepted onto a PhD programme isn't some kind of achievement... but there's an AWFUL lot of time and effort to be put in before Vee's worthy of using that title, and she's not even started yet.
Honestly, I think I'll have less patience to stick this out for 4+ years than Vee does
Eh...I don't think getting into a programme is that big of an achievement, if I'm honest. I don't know about America, I've only applied/gone through this in England, but for a standard PhD it's pretty easy just getting a place. I don't know anyone ever get rejected for the place itself (except for certain very competitive programmes that usually lead to some kind of accreditation, like clinical psychology for example) it's normally the funding that people don't get and therefore can't take up their place. Oxford and Cambridge are notorious for giving out more places than they will fund for example, I know several people who 'got into Oxbridge PhD programmes' but had to go elsewhere as they only got funding elsewhere. Funding is basically king for PhDs. Obviously she got funding at Claremont and idk anything at all about how difficult it is to get funding in the states but I would assume if she's going there, a not very high profile uni, that she definitely didn't get any funding in England.
And just as an aside on the whole PhD thing anyways...I always say to people I genuinely believe if you're smart enough to do a bachelors, you're smart enough to do a PhD. People think doing a PhD means you're super smart, having done one myself I disagree, and I know plenty of what I would call very intelligent people who did not make it through the PhD. The PhD is basically, in my experience anyways, the ultimate test in resilience and grit. You can be the smartest person in the world and not get through it if you're doing it for the wrong reasons. Wanting the title is not enough to get you through the hardest parts.