I just spoke with Charlie Ahearn this weekend at the panel discussion in NYC for the book "Aerosol Kingdom" (which you should definitely check out) and I asked him about the kitchen scene. The problem was money (I know, big surprise). The people that hold the rights to the two songs used in that small clip wanted $8,000 each, which was far more than Charlie could pony up, especially after all of the other costs of re-releasing a film.
People always think there is some major multi-national corporation behind every project, but in this case it was just Charlie Ahearn (Rhino is distributing, but they don't get involved with the production costs). So, in short, try to understand that sometimes unfortunately money is a real issue, especially when you have real people (not companies) involved.
By the way, the only version that had the original music in it was the theatrical release. The VHS release is the same as the DVD version.
I would HIGHLY recommend that you check out this hip-hop classic for the truest depiction of what it was like back in the day.