It's a heuristic about the complexity of the number. If I have some idea bout the ways that you can come up with numbers, then the vast majority of numbers of low complexity were arrived at with short programs, or through rounding. Short programs tend to be heuristics themselves, and indicate estimates, and thus wide implicit error bars. Often even wider than the reported significance.
As long as there are still people negotiating this way, then it is rational to assume that people negotiate this way some proportion of the time and account for it in your own strategy. It's probably not stable in general.
I get what you're saying, but my point would be that the rounder the number you use, the more you're anchoring your negotiation to the rounding point, and the metric being used here seems to be the outcome of the negotiation. If someone says their price is £45,765 then the anchor is to the single pound. If someone says their price is £45,000 then the anchor is to £1,000s. I think there are both things - complexity and anchoring - at work, but I'd say the anchoring to the rounding point is actually most salient here and don't think it's necessarily much to do with perception of complexity, as attractive as that might be as an explantion.
As long as there are still people negotiating this way, then it is rational to assume that people negotiate this way some proportion of the time and account for it in your own strategy. It's probably not stable in general.