Even the words heard from an ignorant person, if in themselves they be fraught with sense, come to be regarded as pious and wise.
This can be taken in the general sense, but the context of the statement is religion specifically. Indeed, everybody claims to know the truth; however, they arrive at their own concocted conclusion through illogical means and attempt to deceive others for a large following, especially in the kali-yuga.
... a man will be known as a brahmana just by his wearing a thread. ... (ŚB 12.2.3) And one who is very clever at juggling words will be considered a learned scholar. (ŚB 12.2.4)
Even with the Vedic context, it is important to look into these deceptive, twisted interpretations of scripture and realize how unreasonable they really are. As for other beliefs, they must also be held to the same standard, which is what Bhishma says next.
In days of old, Usanas said unto the Daityas this truth, which should remove all doubts, that scriptures are no scriptures if they cannot stand the test of reason.
Any scripture should be supremely logical, for it is not a revelation of the truth otherwise. Obviously, this applies to non-Vedic holy books, but self-critique is just as essential. There cannot be double-standard—if one criticizes another religion for being illogical, then one must apply the same standards, the same test of reason, to one's own faith.
Now, why did Bhishma declare this so emphatically? He was a learned authority himself, and he never deviated from sanatana-dharma. Inspecting not only what he stated at a surface level but its conclusion as well makes something clear: Bhishma implied that the Vedic scriptures are supremely logical.
Indeed, there is no doubt about it.