Not necessarily. For one, most fMRI studies will have a resting state scan to establish a baseline of what an individual's brain is doing in an MRI setting when it's not really doing anything in particular (typically having the subject stare at a fixation cross and letting their mind freely wander). Then, for the actual task, stimuli are presented and responses are recorded at very specific times with that fixation cross in between with enough time for the brain activity to return to that resting "baseline" before the next stimuli.

There's a lot of signal processing theory, regression analysis, etc. that goes in to it. With that said, the issue that arises is that only the strongest correlates may surface or be observed. There may be a lot of brain activity that overlaps or looks identical between that resting state (baseline) and the stimulation state, but can't really be included because a distinction can't be made, which goes back to your final point. That, however, doesn't mean that there aren't actual subsets of brain activity that we can attribute to a specific activity.

For example, if you're in an fMRI and I show you nothing but a fixation cross, then show you a sad image at a specific time for a specific interval, then went back to the fixation cross, and also showed you a scrambled version of that same image, I can (oversimplified) run a diff check to see what's different between the three. From there, I can remove the overlap between the three from normal baseline activity and activity specifically related to visual processing (scrambled image) to reveal what's specifically different with that sad image. If I see that the amygdala has much higher activity during that sad image compared to the fixation cross and the scrambled image, I can conclude that it has some role in emotional processing (well not really in this example because you'd also need a ton of images, including neutral images, with different orderings of each to really be confident; also really couldn't make that conclusion, just present the correlation because...science).

The point is that there are methods to isolate activity related to a specific activity/stimuli/response/etc. However, it's currently very difficult, if not impossible, to make distinctions in those overlapped areas.

Note: this is obviously an oversimplification of neuroimaging research and analysis

The brain is doing multiple things at once. But that doesn't mean its impossible to subset brain activity related to specific activities.

I think I wasn't fair in this comment, because it suggests that it is easy to do, when it actually isn't. For example, a cogntive control task might have an easy and hard condition. You'll end up with significant activation all over the brain for either of them, and their contrast will still have significant differences between the conditions all over the place too (e.g. SMA, pSMA, Anterior Insula, Anterior Cingulate, Posterior Cingulate Cortex, visual and motor cortex, cerebellum, etc. etc. etc.). Because the brain is doing all kinds of things during the task, and any "subroutine" is still going to involve communication between lot of places. But if the idea that function isn't localized, i.e. going back to a naive connectionist paradigm, then, sorry, no. The distribution of activations we get are often quite stereotyped, and if we are more careful and specific with our models we can localize function often even better.