Well, a person can’t read minds.

I can, however, read the text of the White House objection to this bill. They didn’t say, “There is hidden meaning in this measure that we don’t like.”

Instead they said, the measure would “restrict the president’s authority to protect Americans effectively from terrorist attack and bringing terrorists to justice.”

Washington Post

The White House outright said that they don’t like being told they can’t torture people.

It is obvious from your comment that you, like me, believe that torture is a bad thing. It is not obvious from the White House statment that the President agrees with us.

I know that it’s hard to accept, but sometimes the officials we vote for don’t agree with us on every topic. Every official I’ve ever voted for has disappointed me in some way.

Sometimes they are outright liars. During the campaign, they tell us what they think we want to hear, and then we find out from their actions after they are in office that they are not the people we had hoped they would be. Other times, caught up in their own political intrigues, and trying to please their campain donors, they simply fail to live up to their ideals.

You are right to say that politics is a dangerous and complicated game, and there often are hidden agendas behind bills and measures. (boy could I list some examples of that!)

In this case, however, I think that the measure is straightforward. First, 90 senators voted for it, while only 9 voted against. As cynical as I am, I do still think that this kind of overwhelming majority can only come from a good piece of legislation.

Second, here is the text of the ammendment:

SEC. 9011. Congress, consistent with international and United States law, reaffirms that torture of prisoners of war and detainees is illegal and does not reflect the policies of the United States Government or the values of the people of the United States.

Department of Defense website

I honestly can’t find anything subversive in this.
If you want more information about this ammendment, you can read Senator McCain’s statement on his website.

We can never know what our elected officials think, and it wouldn’t be any of our business if we could know it. (I believe in a person’s right to privacy)

All we can know is what they do, but that turns out to be a lot. We all know that power corrupts. So when we hand these powerful jobs to people, it’s our job to watch them, and to give them a correction when they misuse or abuse that power.

If we let them know we’re watching every move, it is a very strong incentive to behave.