I'm not sure I agree with them or their particularly analysis, but I'm very convinced they are different because the way I see it, VC and the public markets are completely different things. It's like the farm system for baseball teams. VC is investing in the upcoming prospects, and the VC is investing in the existing major leaguers. Sometimes you'll have a farm system full of A+++ prospects that pay off huge (Google, Facebook), and sometimes you won't (pick a 5 year period where there were no massive VC payouts). And obviously the returns on those prospects will only go to whatever team they happened to be on (which VC picked them), whereas public market returns can go to anybody. But they are different companies at different ages doing different things. Thus to me it would be quite surprising if their returns were all that correlated.
And at some sense "froth" is irrelevant. A VC doesn't have to sell their Facebook or Google stock when it IPOs, they can hold onto it as long as they like. They are basically investing for the chance to get that amazing stock at a huge discount by getting it at the "prospect" stage, and once it goes public they can ride the public market waves as well.
Generally, there are restrictions in the LP agreements that may limit the amount of the fund that is in publicly-traded securities. There may also be requirements for distribution to the limited partners of public-traded securities.
VCs are paid to make illiquid private investments and massage them through to the point that they are liquid (cash, or marketable securities). LP investors, as a whole, are less than sanguine on the VCs subsequently becoming public markets equities horse-bettors.
I was basing my comment on something a Sequoia partner said that they'd never sold a share of their Google stock, but that might have been their own personal investment (or frankly I have no idea how it works -- do LPs always get cash as returns or do they get shares of the post-IPO stock?).
Unless a special deal is arranged it is cash in, cash out.