I really don't want to beat a dead polygraph horse,
but to be fair, declining to take one actually only "looks bad" in the opinions of those who believe
declining to take one makes you look bad. Likewise, declining a polygraph certainly does not mean you're putting your own worry about it over your missing loved one. It may mean you're following the advice of a legal professional that has advised against taking one.
This is a really good (short) article from a criminal defense attorney that answers this very question:
Should I participate in a lie detector test if asked by police?
And in this particular case, taking one or not taking one really isn't as important, as being asked to take one, declining, but then telling others either, you were never asked, or you took one and passed.
Lying about taking one, or being asked to take one, is what makes you look bad.
Telling people you've been cleared, when the CCSO flat out says no one'se been cleared... it's that kind of stuff that makes you look bad.
jmo