When you said "I didn't reply to any of them".  That's where you gave consent to be charged.  If you examine the messages closely, they inform you you've been signed up and can "opt out" by replying STOP to the message.  Your lack or replying is what gave them permission (because they offered you a way to opt out I guess), hence, no reply = tacit approval to charge your account.  Even if you do reply stop, you'll likely be charged anyway, because these crooks now ignore people who respond to opt out anway....

It's not so much the carrier, but the 3rd party company that's at fault here, but partially it's the fault of the carrier, in so much as they don't do much to stop it, and you... yes you, are partially to blame because you did something, somewhere along the line to invite this scam upon yourself (or some mobile user on your account).  For example, filling out sweepstakes, voting by phone, entering your phone number into an unsecure website for "free" ringtones.  Basically, anything offered to you for free in exchange for some information, (i.e. name, address, phone number, email, etc), gets you onto a list which culminates with a text message from somewhere in the ether that obfuscates the fact that you've been charged.

None of this is accidental.  It's all carfully crafted by these scammers to play on your normal reaction to a normal situation.  For example, the text they send you is meant to easily appear to be a harmless hunk of spam that they KNOW you likely won't look at, and they trick you into it because they KNOW you THINK the charges cannot appear on your bill without your consent.   So you get the number from your carrier and you THINK you have their phone number, but you don't.  You have the number to the company that is a agregator 3rd party billing company, so you ask them for the number to the company that charged you, and the give you the number then, and you STILL don't have the number because that company has a parent company, who is the one to authorize your refund (after they sit on your money for a month or two).  That's if you get the refund.  Often times, you'll find yourself in a game of pass the buck where the carrier, the billing company, the decoy company, and the parent company are all pointing fingers at one another, or just let you yell at some poor sap in the Phillipines who says I'm sorry, can't help you, or hangs up on you because you won't quit and hang up on them.

I must say... I've been with AT&T for 3 years plus now, and I've NEVER ONCE had any 3rd party charge on my bill.... and I've not even install the 3rd party content block onto my account (yet, that's why I'm on the site right now).  Also, I was with T-Mobile for 5 years prior to coming to AT&T, and I never had a problem with them either.  I did get a 3rd party charge once, but it was because I entered my number into a website and got dinged for $10 bucks.  Actually the best 10 bucks I've ever spent, because it prompted me to investigate to the point where I knew how to avoid getting these charges on my bill.  I know my bill amount to the penny, and when it went up 10 cents recently, I noticed it and investigated it (The regulartory fee went up 10 cents).  Anyway, I keep waiting to get hit with something here or there, and it never has happened yet.  With the 3rd party content block in place, I'm pretty safe.

So now everyone knows how to avoid these charges, also check out AT&T's page on 3rd party charges too, it explains it pretty well too.