Why does a Vorta claim to be a Founder in "The Search" Part 2?

Question

In DS9 Season 3, Episode 2 "The Search" Part 2, we hear the following dialogue:

BORATH: Commander Sisko, come in. I've looked forward to meeting you. I am Borath.

SISKO: And you're one of the Founders?

BORATH: That's correct. You seem surprised.

However, we know Borath is a Vorta, not a Changeling.

Why does a Vorta claim to be a founder in "The Search" Part 2?

Answer 1

Three reasons:

1. They wanted to know how much the Federation knew about them. If they called him out on it, then they knew something they try to keep hidden- who the founders are.
2. Deception. It's hard to fight a war if you don't know who's pulling the strings or what their motivations are, especially if you think it's someone who it's not. If they believed the Vorta were behind it, they'd act completely differently to if it was the true Founders. Beyond anything else, it's a great defensive measure. The Federation could fight the Dominion and even defeat them without danger to the Founders if they kept their presence hidden well enough.
3. The Changelings have faced discrimination before. That's why they try to shut the rest of the galaxy out, and their whole motivation behind the Dominion, for aggressive defence. They may believe that people won't respect the Dominion as much if they knew the true identity of the Founders. That may not be true, but that may be what they think given their history.

I suspect this was a concerted effort by the Founders- the Vorta probably have standing orders to pretend to be the Founders to all but their own people, just in case. There are really no downsides given their isolationist attitudes towards solids.