They don't.
AMCAS does collect contact information for your ECs, but they absolutely do not "verify" this like they verify your grades against your transcripts. Any school that you apply to could use the contact info to verify your ECs, but in practice there is NO WAY that occurs either. Unless you set off some alarm bells/there's something particularly suspicious about pieces of your application, no one is going to call to verify that you did 100 hours of hospital volunteering. There's not enough time! Note, this doesn't mean you should be anything but 100% truthful in all parts of your application, but that was probably obvious 😛