Potential employers want to know for certain that the people they are hiring possess the correct credentials to perform the tasks they will be given. Not checking those credentials properly may lead to hiring employees without the necessary skills to manage the job, which then requires the employer to spend time and money on training that wasn't accounted for.
No, people care about other people's credentials. Furthermore, people are not stupid. It is easy to lie and hard to get caught. This does not mean that others do not care. More needs to be done to verify people's identities. However, it is absurd to argue that [people do not care.
No, people are not too lazy or stupid to check credentials. This process can look different depending on what credentials need verification. If it is verified employment, a check only requires a phone call to the previous employer. However, if the person's claims are regarding accomplishments, this can require some further investigation. Depending on the size of a company, this can sometimes be more costly than beneficial, so people neglect to do full fact checking.
I disagree with the comment that those checking security credentials are in some way stupid or unintelligent. In secure places like airports those who check credentials follow a procedure laid out by the company they work for. They undergo extensive training and test to make sure they can be counted on as an employee.