As a guy who plays games, and is now a father, I'll offer my thoughts.
First off, yes, loads of kids play GTA. This is not necessarily right or wrong, but it's up to the parent and how the child reacts. In the TC's case, their child mainly broke the trust - I'd say that's pretty unforgivable. But, nevertheless, it's up to the parent what their child plays.
Before I go any further, I will mention that I think all modern consoles (certainly the Xbox 360 has it) have parental controls. These will allow you to set up accounts for your child (and password-protect other accounts), and only allow them to play certain games, or games that meet a certain age range. Have a look in the manuals, and make sure your console has the latest dashboard updates.
I used to play the original GTA as a teen, and at the time (and even now) I'd say it didn't do me any harm. However, everyone's different. When Superman first appeared on our TV screens there were stories of kids imitating him and injuring themselves in the process, believing they could fly.
Games are no longer just for kids - which is something a lot of people (including retailers - always like going in Smyths and seeing GTA on the shelves next to Peppa Pig) need to realise. Working in GAME in my university years, we'd have loads of kids trying to get their parents to buy them GTA/BMX XXX/Manhunt or whatever the flavour of the month was. Even after saying "this game contains blah blah blah" the parent would normally still say "oh it's just a game" (including one time when a father bought an 18-rated game for his son, and his mother tried to get me fired when his father lied and said I sold it to the son without him knowing - fortunately the till roll proved a credit card was used rather than the cash the father said he gave the son, and I got to hear the mother give the father a right bollocking down the phone when I told her to check the receipt).
For those who are unsure about buying games, I say this - first off, check the age rating, and then also have a look at the back of the game's box. Think: if this was a DVD, would you buy it for your child?
And by the way, yanbu.