How does Nxt agree on a chain when "active accounts" can be easily faked? From what I understand, in Nxt, blocks are mined (or forged) using a system based on Proof-of-Stake where block creation works similarly to a lottery: people have tickets, and the more tickets you have, the greater the chances of winning and therefore forging a block. Tickets in Nxt are just coins you own in the system.

What I don't understand is that for each block creation, the winner is found from a pool of "active accounts" which so happens to be people that are online at that moment. Based on specific things (like how many coins one has), the winner is then found. My concern is that someone can forge a new block without caring about the "active accounts", he sort of pretends that nobody else is online. So he'll mine it for sure, as he's the only one, and then he'll broadcast it. He keeps doing this for the next blocks and so on.

What's stopping other peers from accepting his chain?
Linking to the discussion on the NXT forum https://nxtforum.org/general-discussion/academic-questions-regarding-pos-and-nxt