I half and half agree/disagree. At age 8 I had an Atari ST. At age 10 I had an AST P100 with a Dial Up modem, and I had the privilege to get on whenever I wanted. At 12, I had an NEC Cyrix powered 266 mhz computer, which was my first "gaming machine". It barely ran CS beta 1 at 30 FPS on the Voodoo 3 2000 that was in it. At 13, I built my first machine, an Athlon XP 1.12 ghz with 512 of ram and a GeForce2. This was also about the time DSL went mainstream, and to this day I have the same modem.
During all of this time, my parents gave me my privacy when it came to everything. The most they ever did was walk by every once in a while to see what I was doing. Now that I look back, it helped me build responsibility for myself. As long as your kid isn't abusing anything, I wouldn't worry about stuff like this.