I have read that Electrum never is given your private keys (which makes sense), but I'm still unsure what sacrifices it makes in order to not require you to not store the entire ~14GB blockchain.
So is the gist of it "you make transactions on your own using your information, but we watch the blockchain and tell you anything relevant that happens"? Am I understanding this at all correctly?
If so, who is "we" in that? And can't whoever I am trusting lie to me about how many bitcoins I have?