"Why Are You Here?"

[Kei Fox]

There was that moment before Khan proceeded to torture Chekov and Captain Terrell with the Ceti eels to gain their compliance, the question asked of why they were there still has me thinking of a possible tactful response that could've saved them from being controlled by Khan: The Reliant was passing by what they thought was Ceti Alpha VI and detected the energy signature; they simply were there to investigate it. I always figured that would've been a sufficient answer, without disclosing further info about the more specific details of finding a suitable planet for Project Genesis.
Granted, Khan was intelligent and there was the possibility that he could've discerned that such a response was only a partial answer, a half-truth. And it's possible that he would've proceeded with torturing Chekov and Terrell to gain their cooperation into assisting him in escaping the planet, anyway...

 

[Mr. Laser Beam]

Indeed. Khan was much more suspicious when Chekov and Terrell refused to say anything, than he would have been if they had made up an excuse. They should have been able to bluff their way out.

Although you're also right in that Khan would have used the eels on them anyway, since he would have proceeded with taking over the Reliant no matter what Chekov and Terrell told him.