Trustworthy people are usually quite trusting, and vice versa.

I had two reactions when I read your anecdote. One was, I fully agree with "Julie". But then, I thought about a contest at work I recently was involved with in the capacity of "independent" person. I was asked to think of 10 numbers between 1 and 1000. These numbers corresponded to a list of names in an Excel spreadsheet which were entered in a draw. As it happens, the very first number I drew happened to be my manager's! Now, this was completely independent, documented and witnessed by yet another person. However, I think it's obvious what the concern is about my drawing my manager's name. Regardless, in a large corporation (which ours is) there would be a perception that the draw was skewed.
So, in Julie's case, what would happen if she just happened to draw her firm's name first albeit in a fair manner? Then the other person would then feel that their mistrust was warranted regardless of what the procedure was.
(By the way, we ended up removing any of my team members from the list. Which meant that no one on my team could participate. And that results in a certain degree of unfairness to meet people's perception of trustworthiness because no one on my team could participate even though many of my team members had nothing to do with the particular initiative that was using the draw as an incentive)

It seems to me that, in general terms, Lawyers seem to make their money from an adversarial system. So it's not at all surprising to me that Julie's colleague was so apparently distrusting.