when 'that' must be overt

In his book, Radford presented the exercise that concerns explicit appearance of the complementizer 'that'.

1. I said that/# I would assume full responsibility.
(# means null status of complementizer.)

2. Mike grunted that he was tired.
(Radford indicates that null element instead of 'that' marks ungrammaticality.)

The author wants readers to find out what rule or explanation is possible for each sentence.
Concerning1, it seems easy to solve since the complementizer can be either filled or empty.

However, in the case of 2 sentence, I just can't conceive any plausible idea to explain the explicitness of 'that'.
Would you give a helping hand about this trick?