This isn't really the intended use case, sshing from your Koding VM to other servers. However the VM we give you is yours - you have root and full control over it, if there is something on there to capture your passwords then you put it there :) (We are not the NSA)
That is the least convincing security statement I've heard in a long time. So what if we have root access? You can still log everything or compromise the vm under the hood -- and there really is no way to prove otherwise AFAICT (trusting trust and whatnot). In this case, the NSA would least of my concerns!