You still have to trust the servers. Although the clients verify the PoW so servers have to compute a proof of work if they want to fake some things. Apart from that they can lie by omission and spy on you.
But still by connecting to multiple random servers the probability of faking blockchain decreases.
It's like playing russian rouletted with 6 barrel gun, vs playing with 100 barrel gun. With 100 barrels it's still dangerous, but the probability of failure decreases considerably.
If you outnumber the fake servers 100 to 1, and connect randomly to multiple ones, then that risk is avoided.
That doesn't prove anything, an attacker could spin up lots of their own servers and DDOS all the other ones so you only connect to them.
A sybil attack can be detected, by the servers reporting the DDOS to the devs, by looking at the donation bitcoin address of the servers and the taint between them, and the IP address.
If you are extra cautious, then check the address balance via a secondary API from services like blockchain.info.