The support from both the Empire and the Federation is enough to prove his connections and influence, far more intimidating than simply appearing at the Dinner at Dusk without a ripple.
However, the statements from these two parties are not out of regard for him.
Adam does not yet know about the Star Alliance's meddling and only thinks that Heckler ambushed him, believing that the situation is still within a controllable range, which is why he issued a statement.
On the Federation side, they were initially reluctant, as issuing a statement would inevitably require a subsequent result.
If not, it would be like staking their reputation to guarantee someone else, something they have done before, but prefer to do as little as possible.
However, the Empire had already made its statement, which gave the Federation a slight sense of assurance.
Moreover, the Star Gate Node where the ambush occurred is considered their actual control area, which also somewhat challenges their authority.
