I had a much larger post planned, but then I ran some numbers. Long story short, I agree

Using
CoatOSilver's bucket theories (which IMO are incredibly solid, it's the only thing that explains variance in influence levels when no commanders act in a system for a whole tick) I admittedly expected to see some significant differences between values as I applied changes. But the results honestly surprised me a little.
Basically, if you apply positive and negative actions at the same time, you get an exact transfer, but I don't think that's the case. Keeping it simple, we know (from livestreams) there's different buckets for positive and negative actions. I think it applies one set of changes (Positive, for arguments sake) and then applies the other (negative) i.e empties one "bucket" of changes, then empties the other bucket of changes.
I ran with a bucket size of 200, and faction influences A(55%), B(15%), C(10%), D(10%), E(10%). Applying 5 points of positive work to faction D and 5 points of negative work to faction A (first the positive, then the negative) the resultant influences are:
A(52.53%), B(15.01%), C(10.01%), D(12.45%), E(10.01%)
If we run with negative first, we get *closer* but not exact:
A(52.47%), B(15.01%), C(10.01%), D(12.51%), E(10.01%)
Finally, if we inverse the numbers on these results (i.e do a second tick with 5 points negative to D and 5 points positive to A) we get close to, but not exactly the same result.
A(55.00%), B(15.01%), C(10.01%), D(9.95%), E(10.01%)
Interestingly, this becomes much more skewed (in neither A or D's favour, but D is hit harder) if we up the amount of points traded in both ticks to 30
A(54.85%), B(15.70%), C(10.47%), D(8.5%), E(10.47%)
These results don't include the rounding that goes on according to CoatOSilver's theory; I didn't bother and just punched in big fractions in a spreadsheet. No doubt the impact of rounding would have even more effect on the, well, "chaos" of these numbers.