Don't volunteer for anything!
I'm here to tell you, with confidence, ignore it! You're being told this by folks who think they're giving you good advice for self-preservation. One of the most important things to remember is that it's not about you.
One of our Air Force Core Values is "Service Before Self." While self-preservation may be your goal during the first couple of weeks, you'll soon realize (as your MTI will stress) that you can't succeed unless you work together. The sooner you relinquish control, the better. The sooner you start helping others without being asked or told to do so, the better. Your experience will be exponentially better when you and your flight mates begin pulling each other's workloads.
This "Don't Volunteer" advice is frequently dispensed to trainees inquiring about jobs and duties in the dorm. Guess what? Your MTI already has an idea in his/her head about what they think you're going to do, and they're in control. My MTI went around the dorm and asked us questions about our civilian jobs, education, and experience. Based on that and how he'd seen us perform, he assigned our jobs. There was no discussion about what I wanted to do. Sure, when it came to filling the last few things, he did ask for volunteers. Don't be the person that's sitting and waiting, hoping not to be noticed. Volunteer!
BMT, like life in general, lives off the philosophy that what you put into it is what you get out of it. You may question why you should volunteer, why you should keep extending yourself to extra KP duty on Sunday or squadron clean-up, when there are other trainees sitting around your flight, trying to do as little as possible. Surprise, surprise - they ultimately get nothing out of it.
As a Dorm Chief, I had a significant amount of influence with my MTI. My element leaders and I wrote nightly letters to him, discussing the "Trainees of Note" and the "Trainees of Concern." We highlighted those who were always volunteering, assisting others without prompts, and who were consistent performers in our flight. Those efforts did not go unnoticed, and those trainees ended up receiving bonus/privilege phone calls of 15 - 20 minutes. Some were even able to "save" those calls for a special occasion, like a child's birthday. Over 8.5 weeks, you're only going to get (as long as you don't mess up) a 15 minute phone call, once a week. Trust me, you'll want a bonus call if you can get one!
Even in the operational Air Force, leadership values volunteerism. When you're being evaluated, you'll submit a list of your volunteer activities, in addition to your accomplishments on the job. Service Before Self permeates everything we do. Remember that and RAISE YOUR HAND!