Was that actually proven?
It follows directly from the mechanics. See
Steve post here as well as
empirical testing done here. This documentation is actually hard to find, since the feature was added much later than the main ground combat mechanics, but it is there.
For sake of example, consider a formation of 5,000 tons, with one or two INF+HQ5 command units (25 tons each) and the rest INF+PW (5 tons each). The HQ5 units are built as non-combat, which confers a 80% reduction in size for targeting purposes (i.e., enemy units are 20% as likely to target an element of this unit type) as well as an 80% penalty to firing accuracy. This means that the HQ is treated as a 5-ton unit for targeting purposes, rather than a 25-ton unit.
So for a formation with 1 HQ and 995 PW infantry, the probability for the HQ to be targeted if this formation is targeted is: (1*5) / (1*5 + 995*5) = 0.1004%.
For a formation with 2 HQ and 990 PW infantry, the probability for the HQ to be targeted if this formation is targeted is: (2*5) / (2*5 + 990*5) = 0.2016%. Since there are two HQs, there is a relative 50% chance for the formation commander to be killed if a HQ unit is destroyed, relative to the single-HQ formation, so the odds of the commander being killed are 0.1008% - as I said,
slightly higher.
I have noted that commanders of ground formations do not always die when their HQs are destroyed, but if there is some fixed multiplier it should not change the math at all.
Now, there
may possibly be some effect for preserving the overall HQ chain of command even if the commander dies. As far as I can tell, this is difficult and quite likely impossible to show theoretically for a general case because the overall loss rate of the formation(s) involved is necessary to include in a calculation, but it
might be a present effect. However, the fact that HQ elements are so expensive (4x as much as any other component except STOs) means that it is not really worth it, IMO, as you usually need to squeeze every BP of ground units you can out of your training centers to build a large enough army to assault a NPR home world.