FAR 137.29(b) exempts operators in general from the operational regulation extended by FAR 91. It does not excuse the requirement to meet all conformity requirements with approved data, however.
TBO is a recommendation, not a manufacturers mandatory replacement time. Therefore, even under FAR 91, it is not mandatory, and has no bearing on the subject. Any Part 91 operation may continue beyond TBO, and many do, as do many 135 operators and 121 operators (yes, they do).
I have flown for several certificate operators who extended engine TBO's. One operator in particular single handedly extended a well known engine TBO by 400 hours, incrementally, and we were working on 100 more when I left. Again, TBO is not a mandatory time specified by a manufacturer, and is not applicable as given under 91.403(c).
For operations under 121 and 135, TBO is limiting, but may be extended in accordance with the maintenance program for each operator, and it frequently is. In fact, this is often the way in which TBO's for particular powerplants are proven out, and extended, generally. The documentation provided by certificate holders in conjunction with an approved inspection program (and tear down program, as appropriate) is often the basis for increases in TBO for a particular engine type.
Ag operators still conform to annual inspections, and to applicable airworthiness directives, and other requirements provided by the FAR, and by the manufacturer. Individual rotables and components are still subject to mandatory inspection, replacement, service, etc. Each operator for whom I've flown and worked has complied in detail, just as much as any 121 or 135 operator. I've had experience in a variety of different operations under FAR 137, including specific schooling, as both pilot and mechanic. I've never worked with an operator, or for an operator, who didn't shoot for the highest degree of maintenance in these operations. Those of us who do it, know our lives depend upon it.
The military observes specific proceedures and limitations in accordance with the regulations provided (Technical Orders, etc) for each aircraft, and branch.
"This is a particular problem on military turbine helicopters that hit the civillian market because the Army does not typically log the engine cycles. Even if somebody wanted to follow the regs under 91 it would be impossible because you would not know where to start unless you installed a civillian engine, or overhauled every rotable. "
This is the case with all military equipment transferred to the civil sector. I've flown a number of aircraft transferred out of military service into civillian use, and public use. Very often obtaining type certificate data, or achieving conformance with certification requirements, is difficult or impossible. This applies to rotables as well as airframes, powerplants, etc. I've operated enough of that equipment under FAR 137, in fact, that I'm quite familiar with the difficulties, restrictions, and hazards. Most of the time, military equipment transferred to civillian use cannot meet the specific category certification that civillian certificated aircraft can, and the subsequent use of that equipment is very limited. It isn't just helicopters.
However, the issue isn't one of prior documentation. A more basic issue arises as to the origional certification of the product, which is seldom in conformity with the applicable type certification regulations. In order to obtain primary, standard, utility, transport, etc category certification, a complete testing and certification process must be done to bring those aircraft into conformity. With much of this data unavailable or unperformed, the cost of certifying most military aircraft is entirely prohibitive, and the aircraft remain in restricted category, exhibition category, etc.
In the case of several military aircraft I've flown, we've completely recertificated the aircraft as a new type, in accordance with the modifications we have performed for the specific mission, and achieved a unique certification status. This is done on a limited and individual basis with a particular set of serial numbers, and not in general. It's difficult, but possible.