Or in other words, the fact that one person can be twice as fast as another person in the 100m dash does not make it meaningful to say that one person is twice as athletic as another. In particular, we don't expect the person who is twice as fast to also be twice as flexible or throw the shot-put twice as far, even if those can be made true statements for small (e.g. 5%) difference with appropriate multiplicative factors (e.g., a 5% increase in top-speed predicts a 10% = 2*5% increase in shot-put distance).
It does make it meaningful to say they are twice as fast, though. Which provides a basis for discussing improvements to the general factor. Since there are meaningful zeroes for speed or flexibility or throw distance, it must also be meaningful to discuss doubling the effect of fitness on them. Whether it works out in practice is the question, but it is meaningful and not nonsense.
I feel like something's gotten switched around here. We can measure reaction time with cardinal numbers. Check.
This makes it meaningful to talk about doubling or halving reaction time. Check.
We could attribute part of reaction time performance to the general factor of intelligence. OK... but this will be variable.
It's not obvious to me that if we allot responsibility for someone's reaction time scores among several factors, perform an intervention, get improved reaction times, perform the same allocation, and calculate that the contribution from g has doubled, that we can then conclude that the subject's g has itself doubled.
We want to measure that g has doubled, and we have no numbers for that.
If the effect of fitness on speed is small (as a fraction of absolute speed), then doubling the effect has little to do with doubling speed. If it's large (order unity), then we don't generically expect to be able to double the effect while staying in the regime where intelligence is well defined. These two notions of double are just completely different --
one is a derivative, one is a magnitude -- and it's a mistake to link them.