A Kalman filter assumes that measurement noise follows a Gaussian distribution, and it continuously updates its estimate of the covariance based on previous observations. Therefore, if you gave it a bunch of very similar observations (like differing by 0.1) for a long time, the covariance would get very narrow. Once the activity spikes appeared, they would not have much influence on the state estimate because the probability distribution would imply they were extremely unlikely events. This would look very similar to a low-pass filter.

Although the Kalman filter retains some aggregate data about past states in its iterated covariance estimate, it is still primarily a recurrence relation where the future state depends on the immediate present, much like a discretized low-pass filter. This is part of why I'm intrigued by the parent article's use of a Kalman filter for this application.