All of pinboard's servers belong to pinboard. All of pinboards hard drives belong to pinboard. All of the bits on those hard drives belong to pinboard.
Your private data on pinboard's server belongs to pinboard. This is how web services work. If the web service couldn't access its own data, it wouldn't be able to operate.
You can only assume that some bits are yours (to use your terms: your private belongings) when it runs on your own service/when your programs are the only ones with access to it.
Pinboard is not a hosting company (a la DigitalOcean), it's a web service, i.e. it's not a hotel, it's not a bank giving you a safe.