Studio, multitrack, voice recordings have been getting pitch corrected for some years now. But it can also be done to non-multitrack, even live recordings done straight to stereo, without affecting the accompaniment. I know, I invented the technique! The same trick can be used to correct wrong notes - as it happens it's harder with recordings of piano than other instruments but it can still be done. Oh, and I can correct out-of-tune notes on piano recordings too.....
If the accompaniment and the voice are in different octaves then it is no problem. If you can tell me you can separate them when in the same range (esp. in unison)--kudos to you and I can congratulate you with invention
Also, usually, piano gets out of tune in a top range when some strings in a note get out of beat. If you want to say you can correct that and synchronyze them all, I will be more than happy to come and learn the technique as your apprentice.
It is possible when the voice and accomp are in the same range. Obviously it relies to an extent on the odd way the human ear works.
The out of tune accompaniment is much less noticable than that of voice