Then run your own node. No one knows which addresses you are looking up for balances, since you are looking them up locally.
Of this I'm agreed. You absolutely need to run your own node to avoid all this mess when it comes to checking the balances of your addresses.
All these sites are doing is broadcasting the transaction via their own node. If you are going to use someone else's node, then you are always going to have to go through them (or some other third party) to do it. If you don't want to do that, then the only remaining option is to run your own node.
I meant that whether you broadcast it through a block chain explorer or directly to the Bitcoin network, it's the same thing privacy-wise[1]. The explorer doesn't know anything just like when your node receives transactions that then re-shares.
I just said that I'm sure you can choose a node and send it directly without any explorers. There was even a project dedicated to broadcasting transactions.
- [ ] Add ability to push transactions to network directly through nodes not third parties.
[1] If everything done through Tor.