"The researcher guessed that the man couldn't speak Korean."
Translation:연구원은 남자가 한국어를 못한다고 추측했어요.
2 things to remember here:
• Korean indirect quotation is not subjected to "time sequencing" as in the English language.
• The quotation is in the present tense.
The form to use for such quote is: VS + (느)ㄴ다고 [main clause].
[VS]-ㄴ다고 - verb ending in vowel
[VS] -는다고 - verb ending in consonant
In the example, Verb is 하다 (abbr. for "speak"). VS is 하 so, the quotation would look:
[...] 하 -ㄴ다고 = [...] 한다고
From what I understand ~ㄹ/을 수 없다 indicates a permanent state of inability.
못 implies an impossibility by current circumstances.
But 할 수 없다고 is grammatically correct.
~ㄹ/을 수 없다 / 있다 are adjectives (adjectival verbs) so in a present tense, indirect quotations it is just a matter of adding -다고 to Verb stem.