And you're safe from the government asking about your transaction? That's kinda surprising. I'd assume they keep your data even though you asked them to delete your account. It is difficult to trust a third-party service to keep its promise to protect user's privacy considering how often a data leak happens, or how often they sold it to other parties.
I didn't feel completely safe at the time, but I had a total of between EUR 2 and 3k of transactions, which if you don't have any other income is tax free, so I've decided to do nothing and hope they don't find the amount interesting enough to start their investigation. If I had more than 10k in withdrawals, I'd quickly pay the tax. According to the tax law if you pay what you owe before they officially inform you of an investigation, you can't be charged. That was probably what they were actually trying to achieve. They wanted to scare people enough so that they'd pay up.
Bottom line, don't send your private data anywhere. If you just use your full name and address, you can always claim it wasn't you and it had to be someone else who knew you and wanted to hide himself behind an alias.
That sounds unrealistic unless you're fine with not using any centralized service at all. Wouldn't you risk getting a fine or something similar if you're trying to lie your way through it though? I'd rather not use any service at all if that is the case.
Not "any service at all" just not using a centralized bitcoin exchange that requires KYC. Some exchanges don't require it as long as you stay below a certain threshold. In the EU it's 1k Euro.
You can in fact find exchanges and ATMs where you can withdraw up to that limit anonymously.
