Really? I see no connection between the two. explain more? Perhaps honesty. Not integrity. More likely good marketing skills. "Nothing shouts "good marketing skills!" more than sharing failure.
They're VC's... so a much higher standard of proof is required to establish integrity. (cough cough Eduardo Saverin)
Gotta remember, all angels and VCs are desperate to increase their "deal flow", that means they need startups to know their name when they go looking for money. So the VC puts on a sort of phoney humility... a kind of "hey we're worth billions but same as you its been hard!" type thing. "Look at how we made mistakes where instead of making tens of billions we only made billions". That way when you are looking for money you might think "Hey those Bessemer guys seemed pretty down to earth, like me!"
It's more like a good PR agency wrote it than 'refreshing'. No one there actually writes... they're al playing golf. It was Sally at the PR agency who wrote the thing that evoked a sense of integrity from you. She needs a pay rise.
integrity being, "the quality of being honest and having strong moral principles."
okay, so, I don't have hard evidence of their strong moral principles, that said, to be in the VC business that long must be a fairly good indicator that their services are trusted, and their behaviour is befitting of their duty.
"With $4 billion under management, Bessemer invests from $100,000 to $75 million in innovative companies like LinkedIn, Yelp, Skype, CornerstoneOnDemand, Pinterest, Box and Twilio. Over 100 Bessemer companies have gone public. Last year alone, Bessemer had 5 IPOs, 7 M&A exits, and 20 new investments. "