I've always figured the sooner you let the person know you're human, the better.
IMO, it's better to make a faux pas right up front to break the ice. Drop something, bump into a door, make a joke about it and move on. Now you've put the other person at ease because now they don't have to be as careful
You're right, I don't know where your former colleague thought herself an expert. I'd be unimpressed if for 3 or 4 times in a row you never even got to talk to the person. What if after that time you realize you're not a good fit? Now you've wasted all that time you could have been having fun getting to know someone else. It also sets up the expectation that there's not going to be a lot of communication.
If I or the other person is going to mess up, I'd rather have it happen first or 2nd date.
Keep in mind though, my idea of messing up gives a lot of leaway.
From my dating days, 2 that come to mind, that never made it to a 2nd date...
One guy spent the entire night bringing up how I would be such a good mother. Even after telling him I wasn't ever going to have kids.
The other one told me all about all the different toilets he used while he was in Europe.
I had plenty of other dates though, where everything didn't go perfect, and that's what made them so great.
The first great love of my life met me for our first date by climbing out of his dorm room window to where I had stopped to talk to someone. He fell flat on his face.
Later, I climbed back with him through the same window, into the room. Hubba hubba. We were together for about 8 years after that.
Messes are fun. It shows us for who we are.