And I hope we do not have a discussion about whether you can exchange an entry stamp for a different visa at a local immigrations office? This really is established knowledge.
can you find this rule anywhere published? No. That should tell you enough, whatever the agent says.
And you're asking in a group where the steady crew knows more about visa and immigrations matters than immigrations themselves, even about things they have no personal experience with. Wouldn't you think that if this rule existed, the people who know all the ins and outs of the system, would know this too? I think we deserve a little more trust.
if that would indeed be what the immigrations officer said, then taking the advice would be an reasonable way forward. Although even then, asking for potential different ways here in the group could reveal something (we know it doesn't, but we know the answer to the question; there certainly are situations where immigrations doesn't tell you the whole story).
But now that they are so wrong, wouldn't you agree that his seeking for confirmation in a group where people know this was useful?
Unfortunately the immigrations officers at the airport misinformed you. You cannot exchange stamps with immigrations, neither at the airport nor locally. You really need to leave the country to activate the DTV.