Filtered Signal vs File Compression Paradox
+1 on very interesting and insightful experiment.

Some thoughts:


It's not true that filtered signal has less information. It depends on your input signal, filter type,  and cut-off frequency.
When you high-pass the noisy signal, you're removing the slowly changing components. That makes your signal composed of 'more frequently changing random numbers', thus more random. Of course, that depends if your input signal contains high frequencies or not. Your input is noise, so contains every high frequency. But if your input is a more ordered signal, it will lose much of its energy after a certain HP cut-off frequency, the output becomes near zero, less random, less size.  I think if you increase the cut-off frequency of your HP filter pretty high, after a certain point, the file size will decrease.
One other experiment would be to pass the signal through a LP filter with a low cutoff frequency and see the difference. 
Based on the same theory in 1., you're high-passing your signal, essentially removing the DC part, xc, and leaving it with noise xr.