Omission can present knowledge as a general quality rather than as knowledge of one specified object. This does not automatically amount to a formally quantified claim about every possible thing.
In the account attributed to al-Sakkākī, a rhetorical address rather than a strict demonstrative context may also yield an effect of generality. The listener is discouraged from arbitrarily restricting the statement to one assumed object.
For comparison, “he knows” can characterize a person as knowledgeable, while “he knows this problem” predicates knowledge of a specific subject. Both are grammatical, but their rhetorical range differs.