What is the boundary between beef aging and its decay?

Here is what some will definitely label a biased description of aging and packing that might help a bit. It goes into the difference between wet and dry aging and gas packing which has become more common.

My description of dry aging, and wet aging for that matter, and how I was taught to think of it is that it is decay, but controlled. Enzyme action breaking down tissue for a more tender product, and and improved and more concentrated flavor is the goal and this enzyme action is definitely decay. As to bacteria, even the above article a supporter of aging, in its description of dry aging points out that the outer layer absolutely is contaminated by bacteria.

During the dry aging process, mold and bacteria forms on the outermost layers of the beef which must be cut off and thrown away.

Also, the dry aging is done at 30-35 degrees (F), an area of slow bacterial growth and outside of the 40-140 (F) danger zone of fast growth.

Wet aging is also done, or at least should be, at these same "safe" temperatures and is normally done is vacuum sealed bags so should again not be high risk for contamination. Dry is at more risk because it is in less sealed environment, but is also high price/high value so tends to be carefully inspected and cared for. As normally 10-15% weight is lost during dry curing, and additional is lost to trimming for safety, plus the additional holding time and handling, prices are much higher.

ETA: Their description of 10-11 days for dry aging I would definitely put at the low end of premium aging. All descriptions I know of that is about the limit of water loss, but only the beginning of some of them big changes in flavor.