I have the same thing on my PC, which I upgraded with an SSD a while ago. Actually, I used to until just a few days ago.
Your SSD drives appear in the icon because of your SATA controller's hotplugging capability which is part of the AHCI specification and actually allows connecting and disconnecting HDs from the running system (good for eSATA). The icon itself isn't really a problem, just a bit of an annoyance.
Enabling or disabling "safely remove" won't affect the icon, that only refers to whether you can unplug USB sticks etc. without having to explicitly use the safely-remove icon first.
I'm actually pretty sure Windows wouldn't let you eject your OS drive since it's running from it, even if you tried to do so. As for other partitions on the same SSD, I'm not so sure - but even then, an accidental eject wouldn't hurt the data, it would just force you to have to reboot just to see it again (I'm assuming).
When I installed my SSD, I first used the built-in MSAHCI driver and had that icon. A few days ago I installed the latest IASTOR driver from Intel instead (my SATA controller is an ICH7R) and the icon vanished, leading me to believe that Intel's driver is smart enough not to enable hotplugging for internal drives (or just not telling Windows about it).