If a PC is at wounded 3 and is brought to 0 HP, they fall unconscious and gain dying 4. Most PCs die when they reach dying 4, so the player would like to avoid this by spending all of their hero points.
The hero point rules say that you can (emphasis added)
[s]pend all your Hero Points (minimum 1) to avoid death. You can do this when your dying condition would increase. You lose the dying condition entirely and stabilize with 0 Hit Points. You don't gain the wounded condition or increase its value from losing the dying condition in this way, but if you already had that condition, you don't lose it or decrease its value.
Is "gaining" the dying condition the same thing as "increasing" the dying condition for this purpose?