By sending your request to your vital records office directly by courier or mail:
1) You do not send personal information over the web.
2) You do not provide sensitive personal information to a non-governmental third party who may in turn transfer that information to more non-governmental parties before it reaches your government office for processing.
Non-government third parties may be small businesses with lax internal security procedures or large foreign owned corporations subject not only to U.S. law, but also to foreign law. Some "facilitating" or "official" services may also be in the business of personal information collection and selling. These companies may promise to keep your personal sensitive information private.
But, any non-governmental third party may change management and policies, or be sold to another entity with different policies and procedures.
Sending your application by courier or mail directly to the government office precludes your reliance on third party security procedures, promises, and policies and procedures that may change.
Non-governmental third parties may or may not provide facilitating services they advertise. In some cases, "facilitating" services may add unnecessary steps and cost to your order.