Can ‘dismissible’ be used this way?

Solution 1:

You are using the phrase correctly. The definition you've quoted is just too narrow.

Dismissible redirects to dismiss in the dictionary, and it shows the following as its 3rd definition:

3.

a. To stop considering; rid one's mind of; dispel: dismissed all thoughts of running for office.

b. To refuse to accept or recognize; reject: dismissed the claim as highly improbable.

You are saying the character believes the notion to capable of being rejected with good reason.

You could also say:

He justifiably believed the idea to be dismissible.

Capable of in your quoted definition just implies that it can be done (but doesn't HAVE to be done).

In other words, inherent to the use of the word dismissible is the notion that it's an option to dismiss it. As opposed to dismissed, past tense, that it already has been dismissed.

It would change the meaning if you said:

He believed the idea to be justifiably dismissed.

This would mean that he was convinced it had already been done and with good reason.