People do a lot of stupid things, but I'd think that failing to recognize an undead threat before it causes a global catastrophe is a bit too stupid.
Did the people have zombie movies? We've seen that trope in dozens of other zombie movies, the people in those movies did not know what zombies existed, just because George Romero didn't exist.
On a more serious note, the issue of zombies being an actual threat despite having a strong military is plausible, even in real life. The zombies, despite their several flaws, have one advantage: they're not human. Think about it. Every single zombie on the planet is united by one goal, to kill every human on the planet. The human race isn't capable of that level of unity, even if the zombies are unintentionally united. The zombies themselves aren't strong, especially if they are alone. But given enough numbers ( and since, from what I've seen you guys post, their infection of China definitely gave them numbers ), they can overwhelm humanity by exploiting humanity's mistakes.
Take for example, Night of the Living Dead, the good remake. The zombies were slow, clumsy, and not strong enough to break down a door. However, they outnumbered the humans, and more importantly, the humans in the cabin were not cooperating. They argued, disagreed, etc. If they cooperated completely, they would have easily survived. However, it's human nature. We, as a species, are not easily capable of cooperating with other people, besides close friends and family, and even these relationships can be strained with the stress surrounding a zombie outbreak.
Remember, I never actually read this, so correct me if I got something wrong.