They view a national anthem in the following way
A national anthem is, in effect, a hymn or a prayer in behalf of a nation
W 2002 9/15 explains some of their reasoning (rather than leaving it to an individual's conscience -
When national anthems are played, usually all a person has to do to show that he shares the sentiments of the song is to stand up. In such cases, Christians remain seated. If they are already standing when the national anthem is played, however, there is no need for them to take the special action of sitting down. It is not as though they had specifically chosen to stand for the anthem. On the other hand, if a group are expected to stand and sing, then merely standing up out of respect but not singing would not constitute sharing in the sentiments of the song.
They are right in saying that a person who stands up when their national anthem is being played is showing that he shares the sentiments of the song but they are not right in claiming that all who do so would be demonstrating these sentiments. Obviously new immigrants or those not even speaking the language could not do so. Then there are those who simply don't support it but do so rather than causing conflict or disrespect. Then there are those who do so simply to comply with the laws requiring them to stand and for no other reason.
The law does not state that by standing during the playing of the national anthem constitutes their support for the song, therefore the org. is wrong in claiming that, in effect, it does.