I've seen this happen. I've also seen where someone hired into a management/planning role with the ability to make offshore decisions can impact things for good or bad. A company I was at long ago, the Director of Engineering insisted on offshoring some non-critical things. It was fine, but it was one of those body shops where you talk to person X and it's likely some complete other group doing the work. The output we were getting out them was so bad and wasting the other engineeers time, we had to push back. The excuses made by the director almost made it look like they were getting kickbacks.

Same company, different oursourcing situation - needed some critical low level (assembler) code written. Outsourced to a different region, the developers understood what was needed and turned things around much faster than expected. A small consultancy instead of one of the body shops.