Okay so, stats are calculated thus:
Which means, to create a simple model using a level 100 Pokemon with a base speed (for example) stat of exactly 100, with zero EVs and zero IVs,
we would have its speed as [{(2x100+0+0)x 100}/100] + 5, and all of that into nature multiplier.
That is 205 x Nature. Now if it is as sumwun says, and it is actually multiplied by 99/100, then the result is 204.95
Now, in stat calculation as seen here
The stat is rounded down if the result is a decimal. The stat is also rounded down before the Nature multiplier, if any, is applied.
Meaning the 204.95 drops down to 204, meaning a loss of 1 unit from what should be calculated value of 205. This will mean that invariably, even if by one point, neutral nature Pokemon are missing out.
That is part one, till where facts are available.
Part Two:
Conjecture
This part is based on the assumption that what Bulbapedia has stated is true:
Every Nature represents one of the 25 unique possible combinations of stat increase and decrease; thus, there are five Natures that have no effect on the Pokémon's stat growth as they technically increase and decrease the same stat (Bashful, Docile, Hardy, Quirky, and Serious).
and
The stat is rounded down if the result is a decimal. The stat is also rounded down before the Nature multiplier, if any, is applied.
If we consider these two phrases, then a simpler alternative comes into play:
The Nature Multiplier for the five natures are unity, or one
Taking that idea, then it is simple to see how neutral natures do not affect the stat at all, because the game uses multiplier, which is a single value. And obviously, as we all know, multiplying any value with one gives the exact same number. Now, I'm no coding expert, but if you can assign a multiplier to each nature as 1.1 or 0.9, then just as simply the multiplier can simply be 1.0, instead of 99/100, which is 0.99. This also makes sense if there is a strict line of coding that allows just 3 characters to define the multiplier, with the middle character set as a decimal value, leaving the first and last to have 0,1 or 1,9 respectively. If my idea is correct, then the last digit can also be a 0, meaning a 1.0 multiplier is perfectly possible.
Again, if there is a character limit of 3 (decimal inclusive) then 0.99 can not be a valid combination. Again, this is confirmed only by looking at that exact line of code, and that will reveal if part 1 is correct, or if my hypothesis holds water. Either way, the loss is by one single point at the most.
Of course, there is, to be honest, no way to prove it, as fizz's edit wants, but I thought this was an idea that I could put as an answer. One particular strength behind this is that it views the nature multiplier as just that, a multiplying factor that is not directly added or subtracted from a stat. I tried focusing on how the stat is affected by the multiplier, so I thought this could shed some light. Feel free to leave comments below if you agree or disagree, and we'll make try to make changes as it develops.