We have had several solar cycles with satellites in orbit, and they still seem to be working.
Most important satellites are heavily radiation hardened, and have numerous redundant systems. When they cost upwards of $1 billion, you don't take chances with this sort of things. Most rely on technology from the 60's as it's so well documented and flight proven.
While yes, he is correct the sun could damage a significant portion of satellites, It's one of those things, like tsunami's could hit japan. It happens, and it happens in different orders of severity. So you plan accordingly.
Honestly I wouldn't be so worried about the satellites, as they are designed to function in that kind of extreme environment.
I would worry more about our ground systems, like the electrical grid. Solar storms have been known to induce currents into power lines, strong enough to blow up transformers. (See Canada a decade or so ago) This can take out the electrical grid for significant portions of time, and the grid isn't really designed to handle widespread surges like that.
So I wouldn't get too worked up about this. I don't really know what Michio Kaku was thinking when he did this interview, other than to garner attention with some scare tactics.