I've just skimmed through the posts here, so sorry if this already been said.
This is an issue which always comes up in Govt. circles, and unless agencies are receiving all the paperwork for their employees who are members of schemes - it's neigh on impossible for them to track and prevent this.
The reason why earning points/rewards from govt. travel is discouraged as this can be used by employees as an excuse for not choosing the best fare of the day in order to gain a personal advantage - thus increasing the costs of travel without good reason.
So, if the company/employer doesn't have;
- a specific policy from earning rewards from travel, and
- systems to track and enforce the policy;
and the price of the fare is comparable to other carriers on the route, add your membership number to your booking with wild abandon using the appropriate method for the carrier in question.
And if it's a client who's paid for the fare, just add the membership number anyway. If you get quizzed on it, simply say it was added by the airline who wanted to make sure you received the class of service and recognition you're entitled to with them.
Final note: Let's be honest, most of us in the public service work for agencies where we get bent over backwards and hardly see any extra reward or recognition for our work - so I consider the ability to earn points for govt. travel a small and nice infrequent perk, and will grab them when I've got the chance. Stuff 'em.