There’s nothing wrong with reusing old material on new projects. It’s done all the time in Hollywood. Heck, the Wilhelm Scream has been used over and over again for 60 years. However, if you do recycle material, it’s important to be sure that it was either content that was found on the cutting room floor (and not in the movie itself) or something so small that nobody will notice.
When Michael Bay made his current blockbuster, he did not heed either rule of recycling. Not only is the scene in question part of one of the most exciting sequences in both The Island and Transformers 3, it was so easily distinguishable that even a ton of special effects did nothing to hide the recycling.
Was it budget? No, as the franchise has an unlimited budget for the most part. Was it a mistake? No, as Bay made both movies and is intimately familiar with them. In this case, it was a simple choice made thinking that nobody would notice and even if they did, nobody would care.
This is 2011. The internet makes everything “public” and potentially viral. Poor choice, Michael. Poor choice. If you were going to use something from The Island, you should have had more Scarlett Johansson as a blond.