Learn Spanish (Latin America): Ellos comentan que nadie sabe el chisme. - They comment that nobody knows the gossip.

No, you can't. In English, you can say "They comment nobody knows" or "They comment that nobody knows." In Spanish, the connecting word que is absolutely required to link the reporting verb (comentan) with the rest of the sentence.

Is comentar used the same way as decir for reported speech?

Yes! While decir (to say/tell) is the most common verb for reporting speech, comentar (to comment / to mention) works exactly the same way. It's a great alternative to use when people are casually discussing or remarking on a situation.

I thought Spanish used double negatives. Why isn't there a no before sabe?

Spanish does use double negatives, but the rule depends on where the negative word goes. Because nadie (nobody) comes before the verb sabe in this sentence, a no is not needed. If you put the subject at the end, you would need the double negative: Ellos comentan que no sabe nadie el chisme.

Why is the verb saber used here instead of conocer to mean "knows"?