Well, Eric Carmen claims to have written the interlude himself:
"The song started with the solo. It started 4 bars at a time. Eventually, over a period of 2 months, that entire interlude had been written. Then my quest was to put this in the middle of an actual song. Then it was a matter of trying to figure out what kind of song and how could I do it. I was listening to Rachmaninoff's 2nd piano concerto (written in 1901) and I heard the melody which I used for the verse. Then I needed a chorus. I went back and listened to a song that I had written in 1973 called 'Let's Pretend' for the Raspberries. I just took those notes and took it from there. I thought, ''Let's Pretend' was a nice melody.' The song didn't go quite as far as I thought it should have. I'll go back and steal from myself for this."
He should have checked on the music rights before stealing from the Rachmaninoff estate though.