Maybe? For example, many of the proofs given for "time dilation" seem to demonstrate that time flows differently depending on velocity, but couldn't it be true that clocks (and other phenomena that involve intervals, like waves, molecular transitions, etc.) are impacted by velocity and therefore behave in ways that simply suggest time dilation? How the hell are we supposed to distinguish between the two? Are we simply to take it for granted that time dilation is an observation of how time behaves, and not simply clocks, waves, molecules, etc.?
Likewise for other phenomena that behave in predictable ways, even predictable ways that extend beyond a few limited circumstances. Are we really measuring "time" (that is, a singular thing that exists independently of the phenomena we're observing) or are we simply measuring "intervals" (not singular overarching things, but individual to the objects being measured)? And if we're not measuring "time," wouldn't it be more useful/accurate/honest to say we're simply measuring "intervals" and that those intervals may vary depending on circumstances?
That's not to discount the value of refining these models, since they are useful and have great predictive power. But it's sort of interesting to see how the discoveries are framed, where observations of the behavior of clocks (even very sophisticated "clocks" that use intervals observed in the real world, or are themselves simply real world phenomena) are conflated with observations of the behavior of time.
In the case of the scenario in the OP, it really isn't at all the case that "continuous observation" is what causes the particles not to decay; there's no reason not to clarify this.