does System.currentTimeMillis() return UTC time?

I can confirm that all three calls could depend on the local time, considering the epoch, not the Date.toString() or any similar method. I've seen them depend on local time in specific devices running Android 2.3. I haven't tested them with other devices and android versions. In this case, the local time was set manually.

The only reliable way to get an independent UTC time is requesting a location update using the GPS_PROVIDER. The getTime() value of a location retrieved from NETWORK_PROVIDER also depends on local time. Another option is ping a server that returns a UTC timestamp, for example.

So, what I do is the following:

public static String getUTCstring(Location location) {
    SimpleDateFormat sdf = new SimpleDateFormat("yyyy-MM-dd HH:mm:ss");
    sdf.setTimeZone(TimeZone.getTimeZone("UTC"));
    String date = sdf.format(new Date(location.getTime()));
    // Append the string "UTC" to the date
    if(!date.contains("UTC")) {
        date += " UTC";
    }
    return date;
}

All three of the lines you've shown will give the number of milliseconds since the unix epoch, which is a fixed point in time, not affected by your local time zone.

You say "this time is not the UTC time" - I suspect you've actually diagnosed that incorrectly. I would suggest using epochconverter.com for this. For example, in your example:

1372060916 = Mon, 24 Jun 2013 08:01:56 GMT

We don't know when you generated that value, but unless it was actually at 8:01am UTC, it's a problem with your system clock.

Neither System.currentTimeMillis nor the value within a Date itself are affected by time zone. However, you should be aware that Date.toString() does use the local time zone, which misleads many developers into thinking that a Date is inherently associated with a time zone - it's not, it's just an instant in time, without an associated time zone or even calendar system.