On the current version of busy.org you can do that because they use SteemConnect V1. The new version of busy that is currently in beta also uses SteemConnect V2 and you will have to use your master, owner or active key too.

I contacted Hive account@fabien, one of the creators of busy about the key issue and he said it isn't possible to use SteemConnectV2 with your private posting key.

I can understand that some users are uncomfortable about using their keys on other sites than Steemit. It will get better when SteemConnectV2 is better known.

Remember, that is the whole point of blockchain and crypto space, to be trustless. We should not have to trust your service that it is not storing or using our owner or master keys.

Actually you already trust Steemit with your keys. You don't have to trust my website, you only have to trust SteemConnect. You will be redirected to SteemConnect and you will never enter a private key on dMania. Like I said, SteemConnect is maintained by the Steem Dev Team themselves.