So page 23 "How Destiny Points Are Used" near the end of the section states: "A player can only spend one light side Destiny Point during a single action , […]. The GM likewise is limited to spending one dark side Destiny Point per action."
And the upgrading and downgrading of the pool happens at the same time, though technically you upgrade before you downgrade. This doesn't matter because the GM upgrades the difficulty of player pools by spending destiny points and the players upgrade their characteristics and skills, and vice versa, so no-one is 'downgrading'. Basically both sides just have to make their decision before the dice get rolled. [Addressed p18, second column)
So, yes, it's possible for one side to match the other, LDP for DDP, on rolls. And, in my opinion, I think this is bad gamesmanship and not in the spirit of the game.
But there is a [weak] counter to this behavior. If one side refuses to match for several rolls, and takes a few hits, the balance very much swings in their favor, because that side is now able to dictate WHEN these ***-for-tats happen, and the other side can't activate any abilities that rely on Destiny Points. If discussing this issue with your GM/Players (which ever one is causing the back and forth) doesn't solve the problem, you may want to try this as an alternate strategy for dealing with the issue.
But still, discussion with the 'offending party' is the important first step.
@New Zombie: I tried that houserule, and we (myself as GM and my players) didn't like it because I felt it blocked the players out of playing the destiny points when they felt they should, and led to issues about who declares first or who's destiny point takes priortiy.