The funny thing is that Chopin himself used an entirely different type of rubato, one which is virtually unknown to pianists today.
He would actually keep the left hand very steady, "like the trunk of a tree", while the right hand (melody) we would let freely drift early or late with rubato, "the branches and leaves".
It is very hard to find even old recordings where this is done. Cziffra can be heard using it with Chopin.
The type of rubato you mention is more of the Lisztian variety which ALL pianists use today. This type can be further divided into the groups of robbing the tempo but giving it back at some point (used more for older music), and robbing and not giving it back (later romantic especially).
Anyway, I composed a piece of music where I use Chopin's style of rubato for the main theme, but I actually notated the right hand rubato as rhythmically accurate as possible (without getting ridiculous). Here it is-
As a guitarist, I stand a bit apart from this issue, but from studying Chopin, I am certainly aware of the way that Chopin and his students talked about rubato. It was indeed something that was to be constrained to the right hand, or melody, while the left hand, or accompaniment, kept to a steady beat. We find this account, for example, in Carl Mikuli's introduction to the complete edition of 1879. This works well, I suspect, for a lot of the textures we find in Chopin.
I suspect that this philosophy or methodology of rubato is related to the large influence Italian opera had on Chopin, especially as concerns the melody. It is just what we would hear in the Italian opera house in the early 19th century: the singer taking liberties with the rhythm, but always settling back into synchronization with the orchestra, who have been keeping a steady beat. But this is but one source of rubato and there are others, older and no less important. These other kinds of rubato, where the beat is actually moved forward or delayed according to the musical context, was also something Chopin may have practiced as well. My evidence for this are some accounts of his playing by contemporary musicians, some of whom accused him of stretching out the 3/4 measure of a mazurka so that it almost seemed to have four beats! Berlioz went even further when he wrote in his Memoirs that "Chopin chafed under the restraints of time, and to my mind pushed rhythmic freedom much too far ... Chopin simply could not play in strict time."
Berlioz, we have to understand, is speaking as a conductor and one who was struggling to get European orchestras of the time to both play in tune and play in time! For the truth of it is that all musicians, and all soloists in particular, shape the rhythmic and metric aspect of the music they play. Often, in music that is very motoric, the shaping is very subtle and does not interfere with the 'groove'. But in fantasia-like solo music, the shaping takes over and the notation is really only a sketch. Here are some examples. First, the extreme example of an unmeasured prelude from Louis Couperin, where there are NO rhythms written down. This is from a manuscript dating from 1690, but Louis Couperin died in 1661.
The 'unmeasured' prelude originated on the lute, where, as the pitches and rhythms were notated separately in the tablature of the day, the composer could simply leave out the rhythms. The harpsichordists, tied to vocal notation, simply wrote whole notes to indicate 'free' rhythm. This tradition didn't last long, as composers later on wrote down rhythms. But in genres such as the prelude, fantasia and toccata, we have lots of reason to believe that the rhythms were to be interpreted quite freely. Here is an example
Sorry I couldn't find one with the score, but I think you can hear that there is nothing resembling a steady, reiterated pulse there? This tradition continued with Bach's son, C. P. E. Bach who wrote quite a few fantasias for clavichord. Here we do have the score. As you can see, he puts in a time signature, the 'C' sign that does not actually stand for "common" time, but is a holdover from the medieval time signature "tempus imperfectus" or duple time, indicated by a half-circle. Triple time was indicated by a circle. But as you can also see, there are no barlines! So really, there isn't any meter, at least not at the beginning.
There are also some fantasias by Mozart. Here is one in D minor. Sorry, the clip doesn't have the score, but Mozart does indeed write rhythms in a meter, but gives a different tempo indication every few bars. It starts andante, but a few bars later becomes adagio, then presto.
I have chosen extreme examples to make my point that rubato, in the broader sense of moving the beat around freely, has a long, long history. Nearly every piece of music except some very motoric dance-like pieces, has places where rubato is not only allowed, but probably needed. There is a spectrum from the very free fantasia to the very strict tarantella, for example. But there are also a host of critics calling for the suppression of rubato and they have a good point too. For the truth is, that many less-musical musicians, misuse and overuse rubato. But that's just the way things are!
UPDATE: I just recalled a great quote on the subject by Nicholas Harnancourt: "All notes are created equal--but played unequally!"