It's one thing if a morgue tech says they'll do fine in a zombie apocalypes. It's somehting else when police and military say it. Law Enforcement and Military personnel tend to over state their abilities.
Look at the Watts Riots in L.A. back in 1965. Police thought they could handle it with "no problems". Didn't end well for many people.
Look at the Kent State Massacre, in 1970. Ohio National Guard kills 4 civilians.
Look at the riots in L.A. in 1992 during the trial of the cops that beat Rodney King. The police were in over their heads with the riots. On the 3rd day, National Guardsmen were brought in and on the 4th day US Army soldiers and US Marines were brought in. Between the deaths, and other destruction to the City, yeah... the cops and military were not prepared.
These are just the more well known instances where cops and military have proven that they are not as "ready" as they like to claim.
Fact is, and one that is often overlooked: when it comes to zombies, this is extremely new territory. We REALLY don't know what they will be like, what will cause them, how they spread, and how they can be stopped. We don't know their biology. We don't know if they breath. We don't know if they'll just rot away after a certain amount of time without feeding... heck, we don't even know if they HAVE to feed. All we do "know" about them is from books and movies, which is to say... nothing.
Don't get me wrong. I love zombies. But when it comes to the end of humanity, we need to be realistic. And that means business as usual from the Government. Meaning, when they first find out about the outbreak (days/weeks after "patient zero"), they'll do all they can to have a media blackout on the subject. They'll make sure that not everything is reported, and what does get reported is all "unconfirmed attacks". They'll spend the next few weeks trying to figure out exactly what is going on, and when they find out it's zombies, they'll take even more time to wrap their heads around that.
It'll be a month (at the extreme earliest) before they send anyone to "deal" with the situation. They'll attemp to "contain" it, and when that fails, they'll nuke the area and beyond - to ensure it doesn't spread. Too many people give too much credit to the Government, military and police for being able to handle any situation.... properly.