It means the DA may not file charges under Vehicle Code section 23152(b), or if they do you have a fantastic case.
However, they can still file under 23152(a) which states that one is under the influence for purposes of driving when their ability to operate a motor vehicle is SO impaired that they cannot drive with the caution and care of a sober person. This will depend on "the totality of the circumstances:" your BAC, driving pattern, field sobriety tests, etc.
Whether or not you go to trial is ultimately your decision. Seek the advice of local experienced DUI counsel.
As for the DMV hearing, you or your attorney can try to petition DMV for a hearing. However, you might get a "set aside" given the low BAC.
DMV has a hearing process that is completely separate from the criminal case.
With breath tests, the officer usually writes the results right on the form that goes to DMV. Blood test results aren't available immediately because the lab has to perform the test.
When DMV gets blood test results that are under the legal limit, they usually "set aside" the license suspension action, which means you get your license back.
Your question is a little puzzling because blood results are usually two digits, not three, so a blood result would be .07, not .071. I wonder if this is a test from a handheld breath device.
If you're under 21 (or on DMV probation for a prior DUI), the limit is .01 percent... so a .07 would result in a one-year suspension, even if the DA decided not to prosecute for DUI.
When you're charged with a DUI, there are two separate hearings: the DMV/APS hearing and the criminal court hearing.
During the criminal court hearing, the DA or City Attorney (depending on where your charge was filed) can charge you for driving under the influence of alcohol or drugs or both - that means that even if you had a .05 BAC you could be charged (see Mr. Shapiro's comment re the (a) count). This happens often in cities where the DA's are tough on DUI's, and may or may not happen in your case, it really depends on the individual circumstances.
With respect to your license and the DMV, they have their own hearing for your suspension. If you didnt request a hearing within 10 days, your attorney might (slight chance) be able to still request a hearing. Even if you have a hearing, your license may still be suspended, it all
depends on the facts of your case.
Its best to seek a local DUI attorney who can give you a consultation and give you more individualized feedback after hearing the specifics of your case.