You don't have to disclose capabilities in a press release honestly unless you really, really need to convince people that you're not falsifying the information or trying to mislead people - there is almost no incentive I can think of to mislead people on a general civilian search mission though. A government could simply point some lowly persons to the general area without any explanation of its methods, put almost no official support in funding the search, and it could relieve a great deal of pain and suffering should it lead to findings. The issue may come down to all the scrutiny that could happen were the information lead to the discovery of the plane and (presumably) its passengers. I'm not aware of any government issuing statements like this though in any capacity honestly. It is probably better to assume that our governments, while powerful, are not without their limitations whether it's bureaucracy, technicalities, or simple funding limits.
> it could relieve a great deal of pain and suffering
I confess I don't understand this. The families know how their loved ones died, when, and sort of where (in the ocean). How does knowing the precise location help any?
I think the rituals around death aren't complete without a story. It's the reason why before they tore down the eastern span of the Bay Bridge that let the families of people that died on the bridge visit the spot where they died.
I understand wanting to know more details. But having gone through rituals around death of someone close myself, it doesn't ease any of the pain.
I've also wondered about those families attending the execution of the person who murdered their loved one. I doubt it eases their pain and suffering in the slightest.