False or misleading statements to U.S. Federal Agents (or attornies) is a serious and easily charged FELONY. Thou Shalt Not Lie [or get cute]. Federal agents are broadly defined. I'd assume that a Imigration, Homeland Security officer, and others that aren't FBI, Treasury (Secret Service), or Postal Inspectors would be included.

Saying "I don't know" only works if someone can't show the you might not have "beyond a reasonable doubt" have known.

Even a "casual" comment can be viewed as obstructing if it (mis- or) leads an investigative activity. Personally, I think it is an abomination of piling on crimes on crimes. Really something out of Kafka or Hugo ("Les Miserables"). It's like a "Conspiracy" charge which is piled-on top of relatively minor offense and creates a 10-15 year felony where the underlying "crime" is more like a reckless driving charge than murder. Anyway, if you're interested.

It has implications that go far beyond saying that "I don't have any undeclared items in my luggage"...

It doesn't just deal with your actions, but the knowledge that you might have of others actions. In many cases the crime of "Obstruction" or "False Statments" is a worse crime than the original action. Lying about a misdeamor (which might involve a fine and short time in jail) -- not a felony is not a 10 year or series of felonies that may stem for a "false claims".

Other countries have similar laws. In many cases they don't have "Fifth Amendment" protections.

The case of Martha Stewart is a recent classic example. In her case, she lied about a crime she wouldn't have been convicted of -- but went to jail for lying. In her case she had already talked to a lawyer, and apparently didn't get adequate advice (or didn't listen to it, to be charitable).

http://en.wikipedia.org/wiki/Making_false_statements
http://online.wsj.com/article/SB10001424052702303299604577328102223038294.html (Naughtical or Nautical)
http://corporate.findlaw.com/litigation-disputes/how-to-avoid-going-to-jail-under-18-u-s-c-section-1001-for-lying.htmlhttp://corporate.findlaw.com/litigation-disputes/how-to-avoid-going-to-jail-under-18-u-s-c-section-1001-for-lying.html

In countries where the investigaing magistrate is more like a judge, prosecutor and policeman (examples would include many European countries, or countries that have adopted their judicial and police administrative proceedures) make it even worse. The level of review is an appeal of a judgement where the likelihood of overturning a conviction is much lower.

In many countries, as foreigners travelling together (or in close proximity), in practice, you may not be viewed as acting individually. If you have stuff packed in a boat or a car together, if you stayed in the same room, were in the same vicinity when something was purchased, etc. then presumption of innocence doesn't mean what you might believe.