Can Bitcoin buying be traced?
In some cases, yes it can be.
If you buy bitcoins using cash, it is unlikely to be traced, but as soon as you attach your name to a transaction (buying something from Newegg, for example), the owner of those bitcoins will be known to any agency with enough clout to gather such information.
If you buy bitcoins on an exchange or through a broker like Coinbase or Circle, then you should count on the transactions being traced. And unless you actively launder/mix your bitcoins, it would be trivial to follow the digital trail left by your bitcoins to prove what you use them for later on.
Despite what is reported by mainstream media, Bitcoin is NOT anonymous by default. The digital trail left behind is very traceable, even with basic tools built by amateurs, and undoubtedly those tools and their accuracy will improve with time. Bitcoin can be made fairly anonymous with extra software (dark wallet) and extra care in conducting transactions, but in reality, cash is still king when it comes to anonymous purchasing power.