BBL different approaches: In that you put fat under the muscle versus not? Is this true?

Theoretically, intramuscular fat injections provide a better recipient site for fat graft survival than subcutaneous injections due to the better vascularity of muscle compared to fat.  However, the muscle also has larger arteries and veins, so complications such as hematoma and even more serious implications such as fat emboli are likely to be more common.

Far more important than the technique is the skill and experience of your plastic surgeon. Choose your surgeon rather than the technique and let them explain why one technique may be better than another.  Please visit my page on finding the right doctor at drnichter.com on some suggestions on finding the most qualified Plastic Surgeon for a BBL Always insist on a board certified plastic surgeon. 
Candidates for Buttock Augmentation surgery desire an enhancement in the buttock area to offer a more balanced, defined or shapelier contour to the body. There appears to be two different groups of patients seeking the procedure. One group of patients is younger and has goals of transforming their bodies into more curvaceous figures, like popular Hollywood stars, J. Lo or Beyonce Knowles. The other group of patients is women that have aged and would like to restore a more youthful backside with buttock fullness to replace now sagging areas. Men have also been requesting buttock implants as well.

Techniques will vary especially with regards to BBL. Some grafting planes are without a doubt more dangerous than others.
Fat embolus is a very serious and known complication of fat transfer (which has been recently spotlighted in the media). While it is true, injection of donor fat into the infra-muscular plane (within the muscle) increases fat viability this does come with a significant increase in risk. There are large vessels deep to and within the muscle which can be inadvertently injected while grafting leading to a fat embolus. The consequences of such a complication are very serious and life threatening.
At the recent American Society of Plastic Surgeons Hot Topics, data from AAAASF (ambulatory surgical certifying body) was presented, suggesting that BBL/gluteal lipoaugmentation demonstrates a dramatically higher risk profile than other surgeries. The Aesthetic Surgery and Educational and Research Fund is convening a task force as well. The hope is that we will have more concrete guidelines for addressing these very serious complications.
That being said, the safest way to avoid fat emboli is to stay in the subcutaneous plane (at the expense of fat viability)and avoid the deeper muscular plane. If grafting of the deep plane is planned, surgeons should consider blunt cannulas, aspiration prior to injection. Using a supra-gluteal approach to minimize the risk of inadvertent intravascular injection has also been proposed.
As always, discuss your concerns with a board certified plastic surgeon (ABPS).