Why shouldn't they? When you meet with the advisor, say, "I would like to speak to some of your current students about their experience in the group. Would that be OK?" If they say no, that alone should be a giant red flag. This is someone you're going to be supervised by for years. Good advisors don't take that lightly and want you to have as many opportunities as possible to see if you'll be a good fit.
I once had a professor joke, "The two most important decisions in my life were deciding who to do my PhD under and who I was going to marry. In that order." A bit extreme, perhaps, but it makes the point. You wouldn't buy a car without kicking the tires. If a professor won't let you speak to his or her current students, it's like someone selling a used car who won't let you get an inspection. So go ahead, kick the tires.