The radiation levels near Chernobyl probably aren't that bad anyway; if you lived there, you could probably expect to die of cancer 2-3 decades earlier than normal, I'm guessing. So expect to die at 40-55 maybe. For modern humans, that doesn't sound all that appealing, so we stay away.
But animals don't live that long in the wild typically anyway, and tend to reproduce fairly quickly. So dying of cancer in middle-age probably isn't all that noticeable to them, because they're probably going to die by then anyway, or either accident or predation or (non-radiation-related) disease.
2-3x is likely an overestimate. That may be a good estimate for people who actually lived at the time of the incident, but not for anyone living there today.
But animals don't live that long in the wild typically anyway, and tend to reproduce fairly quickly. So dying of cancer in middle-age probably isn't all that noticeable to them, because they're probably going to die by then anyway, or either accident or predation or (non-radiation-related) disease.