"He could not say that yet."
Translation:Das könne er noch nicht sagen.
The English given was "He could not say that yet" To not accept: "Er konnte das noch nicht sagen," but insist it should start with the direct object, "Das konnte er noch nicht sagen," is weird, and really arbitrary. I wanted to try "Das hat er noch nicht sagen können", but I was pretty sure that wouldn't fly (that is, that Duolingo wouldn't recognize that one.)
Negatory to your last assumption:
"Das hat er noch nicht sagen können" is perfectly fine. :-)
I make up an example:
Someone has to report to the boss in the morning how many delivery's arrived. But this morning he hasn't counted it and can't tell. A third person states: "He could not say/report that yet."
"Er konnte das noch nicht sagen", alternatively:
"Das hat er noch nicht sagen können" "Das konnte er noch nicht sagen" is perfectly fine too.
"Das könne er noch nicht sagen." is also correct but conjuctive, hence different meaning.
Without context hart to say which way to go with the translation. All the above German examples are perfectly correct sentences.
Correct word order would be: "Er könnte das noch nicht sagen." (with the "das" earlier), so that "noch nicht sagen" is together. If we're talking about something in the past, rather than a hypothetical, then "Er konnte das noch nicht sagen."
In this case, however, there are correct possibilities which Duolingo is not recognizing; "er könnte noch nicht das sagen" is not one of them, though, since "das" is misplaced.