How okay is a light deviation from perfect tempo (within phrases, not overall tempo of the piece) for stylistic purposes? Is it even slightly okay, or should you strive for perfectly strict tempo from what's written? (Specific examples in text).

The main case is this: I've been told by a teacher NO, but when I listed to some professional performances it seems like they do it. I will cite the piece I was told no on below, and specific passages in a piece and the recording I'm listening to that sounds like it does below (both pieces are by Chopin).

So first off, I have mainly been self taught. However, I began with a teacher for the first 2 years when I started in grade school so I avoided any completely awful beginner habits, and have had a teacher a few times for a short period in the decade and a half since, most notably during last summer. I play for myself, so I am okay with not being perfect, but I really try to do things right, and when I do have the opportunity for a teacher I pay close attention to fix, improve, and carry the habits over to when I play and practice by myself again.

What brought this to my attention was when I first got my teacher last summer. Because I'm mostly self taught it's kind of hard for me to gauge my skill level, so he had me play around with a few pieces I had looked at so he could see. I played Chopin's Prelude in E Minor, and he stopped me almost immediately. I was slightly swinging the chords in the left hand because I liked the way it sounded, and I had kind of thought that a lot of Chopin gave room for a slight deviation from perfect tempo because of how expressive it was. I will admit that I was overdoing it awfully, and while it probably did sound OK as a separate piece, it did not do the actual piece justice.

However, I have been listening to Chopin's Prelude in D-flat Major (Raindrops) in this recording by Horowitz. When I listen to it, he sounds like he slightly extends the end of the septuplet (? not sure if that's what it's called) in measure 4 at seconds 15-17 in the video. It also sounds like he holds the G-flat that starts measure 10 (at second 34 in the video) a small bit longer instead of making them perfect 8th notes within tempo (and with the E-flat that starts the next measure).

Now, I could be hearing things and this could just be how the music is written to make it sound like this is happening. I am aware that if it is permissible to express the notes in a not-100%-strict tempo as written, it should still be very very close to it (unlike how I was butchering the E Minor prelude).

So, what's the deal with this? Am I hearing things, or is it left up to the performer to embellish the notes a little (stress, little)?

Also, I have been practicing a lot recently, and am taking a stab at the Raindrops prelude right now, so any helpful advice on common problems to avoid for it, or for the piano in general, would be more than welcome.