There's an idiom that goes not worth the paper it's written on:

[Merriam-Webster] : not of real value : not legally valid

(A variation is not worth the paper it's printed on.)

This has a similar connotation to the paper does not refuse ink saying from the question—which leads into my actual answer.

Lee Gesmer, a lawyer, wrote a blog post that added a clever twist to this sentiment in "An Oral Agreement is Only as Good as the Paper It's Written On." Meaning, in short, if it's not put into writing, then it's just words that that don't have any value.

For the purpose of this question, it could be modified slightly:

The spoken word is only as good as the paper it's written on.

The elegance of this is that not only does it use an existing idiom in relation to the written word, but it turns it around to refer to the skeptical nature of speech.

The two idioms actually go well together:

Paper does not refuse ink, and the spoken word is only as good as the paper it's written on.

In short, be skeptical of anything, written or spoken.

There's an idiom that goes not worth the paper it's written on:

[Merriam-Webster] 
: not of real value : not legally valid

(A variation is not worth the paper it's printed on.)

This has a similar connotation to the paper does not refuse ink saying from the question—which leads into my actual answer.

Lee Gesmer, a lawyer, wrote a blog post that added a clever twist to this sentiment in "An Oral Agreement is Only as Good as the Paper It's Written On." Meaning, in short, if it's not put into writing, then it's just words that that don't have any value.

For the purpose of this question, it could be modified slightly:

The spoken word is only as good as the paper it's written on.

The elegance of this is that not only does is it based on an existing idiom in relation to the written word, but it turns it around to refer to the skeptical nature of speech.

The two idioms actually go well together:

Paper does not refuse ink, and the spoken word is only as good as the paper it's written on.

In short, be skeptical of anything, written or spoken.