Coinbase wallets have are secured with private keys LOL, it's just that users don't have any access to it. Every user needs to agree to have wallet not matter if they are from The US or Europe (you don't make sense). As far as I remember you can see the TX ID for each transaction (I wonder if you ever used Coinbase before)
Is it even possible to have a wallet without private keys...?
As for the TX ID, I use the mobile version of coinbase, and you can't see the TX ID nor can you see which address you send or receive your bitcoins. The coinbase app sucks real bad. I can't even see the address when I try to ask for a receiving address, I get a QR code rather.