BME BS + BME Masters vs. Chemical and Biomolecular Engineering BS + BME Masters

Have read some people comments about BME at baccalaureate level not being as complete as it should be. That programs are lacking several aspects that are covered in other fields of Engineering that can prepare students much better for a BME Masters and work opportunities. Many of these people suggest to go better with a Chemical or Electrical Engineering BS and then do your Masters in BME. How accurate are these comments?