Theses are not the same. I agree that rubato is largely an individual affair, but not rhythm.
Agreed, good point. I should have said "interesting sense of rhythm" perhaps.
I realize that we have been down this road before (I think) so I won't press the point but to observe that rhythm is mathematical, defined and given by the composer, the particulars of rubato are not, and rubato affects the tempo, not the rhythm therein.
I would, however, still take issue with this point. Scientifically, there are really only two basic elements that the pianist is controlling: force and duration. Rhythm and tempo are of course subcategories of duration and are thus inextricably linked. That is, because there is really only the one element that one is controlling, what one does to tempo must by definition also affect the rhythm. Consider again the repeating bass-note chords in the Chopin E Minor Prelude. If one applies rubato to that figure, what one is doing in essence is to "steal" time from one portion of the figure and ideally, according to the definition of rubato, make it up elsewhere. So what does stealing time really mean? One might, for example, speed up slightly at one point in the measure and then slow down later on in the measure so that ideally no net time in the measure is lost. However, in addition, during that slight speeding up, effectively what one is actually doing is to lower the value of the eighth notes in question more toward a faster rhythmic grouping such as 16ths, and then vice versa for slowing down, thereby affecting the duration of the rhythmic eighth-note groupings to regain the net, overall effect of tempo. One might think of the rhythm as the nitty-gritty note groupings (i.e., the details) that comprise the whole. The rhythm, the details, fit into the the overall time (tempo, same word). What one does to the whole must in some way affect some of its constituent parts, and vice versa. Just as cutting or adding a piece to a pie affects the conception of the whole pie, so too does manipulating details, in this case, rhythmic elements affect the tempo (i.e., literally the overall time
or duration as delineated above).
The difference between rhythm and tempo, in other words, constitute a semantic distinction that illustrate different facets of the listener's perception related to just one element: duration. When rubato is well applied, one wants to have the perception
that (1) the rhythm is not affected (which is not possible) and (2) the overall tempo is not affected (this is mathematically not really possible for a non-machine, human being). To sum up, at any given time that a musician is not playing mathematically (which besides being boring is strictly impossible anyway), one is affecting only the one factor, duration, and by definition, therefore, both of its subcategories rhythm and tempo.