While we don't have nearly as cool old architecture like other continents, buildings/houses from the 70s are all over. I think most historic buildings tend to be closer to 100+ years old, which is almost half the age of the country.
Depends on where you're at too, in my area there are still houses from the 1700s, but people hadn't even been building houses in LA (where he mentioned) until like what 18-something? The Mexican American war was 1846 and then the gold rush was 1849, so I'd guess somewhere around there. And before that there were whole ass Adobe Villages made by the native population of our country out west (not sure about LA, but), and as the other poster said, they count as history it's just that the europeans came and killed most of the people who knew that history.
Basically, he's just wrong and/or expecting us to have buildings older than our country (which, actually, we do have them and I've been in them. Not older than the colonies though.)
Not just LA, many houses in the US are built like crap. Timber frames with plasterboard walls, easy and cheap to put up but not long lasting. You can sometimes rate the houses in minutes, as in how many minutes it would take to burn entirely to the ground. Many are under 15.
With LA at least they have some good reason, all the earthquakes mean you either build them to last through or you build them to be easily rebuilt.