Yes, your association staff may very well need international trip travel medical insurance if they are traveling to another country. Many insurance policies don't cover international travel, or at least don't cover it well.
The first place to start would be checking with your health insurance company. Ask them if you are covered when in another country. If you are covered, ask them how the deductibles and out-of-network payments apply. Last but not least, ask them if they provide medical evacuation services as part of the policy. Being injured or becoming seriously ill in another country is no fun. Being stuck there because you cannot afford the cost of special medical transportation adds insult to injury.
Even if your health plan covers you internationally, it may not cover all of your expenses. Fortunately, travel medical insurance is very reasonably priced, so there is no need to risk your health or your financial security. Find medical travel insurance.