The Pentagon has gone on record to officially say that they do have satellites that spy on other satellites. The Mitex micro-satellites, which were launched in 2006 have been flying around in the geostationary ring and have made observations of the DSP 23. DSP 23 is a satellite that can monitor missile launches but went offline shortly after reaching orbit.
The UN was particularly upset about the idea of satellites that can track and in theory destroy other satellites. The UN also pointed out that China may be interested in the news as the US has criticized the country and its leaders for a lack of transparency.
At the end of the day many will likely not be surprised by the news. While the US may be the first to admit that it has the capabilities there is a high probability that other countries have the same technology.