This is not exactly true. This isn't really the place to discuss it in much detail, but I will say this. If you have apps running in the background that are draining THAT much battery, then chances are the app is in someway problematic.
Android stores tasks in memory. When you open the apps, they are called from that memory which is actually less resource intensive to get the app back to the foreground. Android handles tasks in a special way. When the operating system feels the need to kill applications to free ram, it will. And does.
IMO you are more likely to see cpu stress slowing things down than used memory, which is why opening applications from memory which are frequently used will likely actually result in LESS power consumption.
When you kill an app and open it the next time, instead of it opening in a "stored" state in memory, you're potentially cycling the cpu more to reopen said application.
NOW, show me a task killer that shows cpu cycles and that background apps are actually cycling the cpu and are not just harmlessly stored in ram and there might be more discussion, or as I said, it could just be an app that needs some adjustment.