Grice on 'inform' as factive

"False information is not an inferior kind of information; it just
is not information."
H. P. Grice, Studies in the Way of Words, p.371.

Unfortunately, I don't seem to agree with Grice on the passage immediately
preceeding that dictum above, with which I DO agree. The passage goes:

The [conversational] maxims [I proposed in Logic and Conversation,
QUANTITY:
Make your contribution as informative as is required
(for the current purposes of the exchange).
Do not make your contribution more informative than is required
QUALITY: try to make your contribution one that is true
Do not say what you believe to be false
Do not say that for which you lack adequate evidence, p.26]

do not seem to be co-ordinate. The maxim of Quality, enjoining
the provision of contributions which are genuine rather than
spurious (truthful rather than mendacious), does not seem to be
just one among a number of recipes for producing contributions;
it seems rather to spell out the difference between something's
being a contribution and (strictly speaking) failing to be,
any kind of contribution at all. op. cit. p.371.

Etc.