No, dating sites should not be held responsible for people (we choose to date). Each and everyone of us chooses our own friends, lovers, and spouse.
Most dating sites only require a form a payment to become a member and others are free. If the government has a difficult time tracking down known terriorists with all the resources they have you can imagine how difficult and expensive it would be for a dating site to do (up to the minute background checks) on thousdands or millions of members!
The same people you'd meet online are the same people going to nightclubs, restaurants, parks, beaches, malls, college, work, grocery stores, and churches. Prior to online dating they were meeting and dating people without being "pre-screened". It's important to always take things slowly when meeting a stranger. It takes time to get to know someone. There's no rush to exchange email addresses, phone numbers, or meet in person. You can communicate through the dating site via their email and IM.
One of the great things about meeting someone online is it's up to YOU to decide when or if you ever meet. This gives you time to get to know the person and even pay to do your own background check if you are so inclined to do so. Every relationship begins with a calculated risk. Keep in mind most people are going to put their "best foot" forward. It takes more time to get to know someone than most people are willing to invest these days. Looking out for #1 is and always will be YOUR responsibility. You shouldn't trust anyone else to do it better than you!