Michael Bay directed both The Island and Transformers 3, so I guess it isn't that surprising that he might have reused some footage. It's pretty common to use "stock footage". Of course directors probably got away with this more often before the advent of the internet and people with far too much time on their hands.
See the clip here for a comparison of two chase scenes - one from The Island and the other from Transformers 3.
- Michael Bay Reuses The Island Footage for Transformers 3 (geeksaresexy.net)
- Recycled Bayhem: Transformers 3 reused a chase scene from The Island [Video] (io9.com)
- Does Transformers 3 Re-Use Footage From The Island? (gizmodo.com.au)
- Michael Bay Reuses a Scene from THE ISLAND in TRANSFORMERS 3 (geektyrant.com)
- Michael Bay Just Re-using Footage from The Island for Transformers 3 [Video] (gawker.com)
- Video: YouTube uploader catches Michael Bay sampling himself for Transformers 3 (autoblog.com)
- Is Michael Bay Afraid To Get Rosie Huntington-Whiteley Dirty? (films.ie)