Theoretically, this is true. The value, and hence the price, is splitted. But markets are not perfectly efficient, and Bitcoin markets in particular are very inefficient and totally driven by psychology, particularly speculation and greed.
This can make you end up with either a larger sum if you buy exactly before and sell shortly after the fork, or a smaller sum. Why should the sum be larger? Because there's people on both sides of the fence (the original coin and the forked coin) which think that their coin will "win the race", thus they include a certain additional, speculative value deducted from assumed future price increases into their estimates of the current value of their preferred coin. This drives up the speculative value of both coins simultaneously, and since either side focuses mostly on its preferred coin, driving up the perceived value of it, and neglects "driving down" the perceived value of the other sides' coin (because of disinterest or simply because driving down perceived value is much harder than driving it up, as humans are usually focused on positive things), this can result in a situation in which the mathematical sum of the speculative value added to both post-fork coins is quite a bit larger than the "combined" speculative value that was previously included in the original coin.
This is, in my opinion, exactly what happened with the Bitcoin Cash fork earlier this year. For this Segwit fork, people saw that the earlier fork "created value out of thin air" and thus began to incorporate some of this assumed future value into their value proposition of the coin pre-fork. This drove the price increase right before the fork (well, partly - there was also the CME news, which was a big driver, too). Funny enough, this time it probably won't work out as it did last time - the fork was "called off", and even if it would happen, it most likely will not result in a similar situation due to a) the "free money" having already been priced in during the time before the fork and b) the fork being a "colliding fork" this time, with both coins wanting to be "the real Bitcoin", having no replay protection or real separation of both networks. They wouldn't have coexisted for long - one of them would have "won" and captured the vast majority of value, while the other one would have diminished to the low 3-digit or even 2-digit price realm (effectively equaling a worthless coin, as in crypto, there is NEVER a really worthless coin in terms of having a price of zero - there is always someone wanting to pay some price, albeit very low, for anything that has "crypto" attached to it ;-) ).
This can make you end up with either a larger sum if you buy exactly before and sell shortly after the fork, or a smaller sum. Why should the sum be larger? Because there's people on both sides of the fence (the original coin and the forked coin) which think that their coin will "win the race", thus they include a certain additional, speculative value deducted from assumed future price increases into their estimates of the current value of their preferred coin. This drives up the speculative value of both coins simultaneously, and since either side focuses mostly on its preferred coin, driving up the perceived value of it, and neglects "driving down" the perceived value of the other sides' coin (because of disinterest or simply because driving down perceived value is much harder than driving it up, as humans are usually focused on positive things), this can result in a situation in which the mathematical sum of the speculative value added to both post-fork coins is quite a bit larger than the "combined" speculative value that was previously included in the original coin.
This is, in my opinion, exactly what happened with the Bitcoin Cash fork earlier this year. For this Segwit fork, people saw that the earlier fork "created value out of thin air" and thus began to incorporate some of this assumed future value into their value proposition of the coin pre-fork. This drove the price increase right before the fork (well, partly - there was also the CME news, which was a big driver, too). Funny enough, this time it probably won't work out as it did last time - the fork was "called off", and even if it would happen, it most likely will not result in a similar situation due to a) the "free money" having already been priced in during the time before the fork and b) the fork being a "colliding fork" this time, with both coins wanting to be "the real Bitcoin", having no replay protection or real separation of both networks. They wouldn't have coexisted for long - one of them would have "won" and captured the vast majority of value, while the other one would have diminished to the low 3-digit or even 2-digit price realm (effectively equaling a worthless coin, as in crypto, there is NEVER a really worthless coin in terms of having a price of zero - there is always someone wanting to pay some price, albeit very low, for anything that has "crypto" attached to it ;-) ).