Maybe you can live with not logging in from a "computer" that you don't fully control in your basement, but in real world, there happens to be a lot of times that you need to login through a computer (and sometimes only available ones are public). On the other hand, it's not over only with control of the computer you used as client. You need the control of the network as well.
General rule of thumb should be, never put anything secret at all to databases that could be accessed over public networks, like Internet. If you don't do that, just admit that the thing is not a secret anymore and live with it.