I'm not too sure where the "bitcoin is anonymous" misinformation comes from, sadly.
Saying that "bitcoin is anonymous" is indeed misleading.
But bitcoin does make it possible to stay anonymous, if you are very careful. For example, you can generate a new address and use it to receive bitcoins without revealing anything about yourself at the time of payment, and without revealing to any third party that you were paid.
Making payments without leaking any information is much more difficult. You would have to pass your bitcoins through a third party which you trust not to reveal the link between deposits and withdrawals. If you don't fully trust any such service, you can pass through multiple independent ones. Even then, somebody could correlate deposits and withdrawals by their size and timing. There exist Mixer Services (https://en.bitcoin.it/wiki/Mixing_service) which are designed to make this difficult.
If anything, this "Bitcoin isn't actually anonymous" is the real misinformation.
Imagine you receive small payments in 100 different addresses and then want to buy a new computer. If you create a single transaction with all those addresses as inputs, you make a big trace of a single owner of all of them.
I myself not worried about that at all - if you have to hide your stuff from someone, then the problem is not in the hiding techniques, but in the threat. Today the biggest threat is the govt, not some thieves whom you don't want to tell when you go to vacation.