While there is some truth to what he's saying, the "danger" involved is highly exhaggerated.
If the putty window is blatantly killed, the client will not be able to send any information/keystrokes/commands that lets the connection terminate cleanly. In effect, the server is left hanging, thinking the client is still there. However, a properly coded protocol will involve a timeout, so the server will eventually just drop the connection.
I've seen some systems that become inaccessible because of this (I believe it was a managed switch running some ancient firmware). For starters it only allowed for one admin to telnet in at a time. Secondly it had a laughably high timout - a couple of hours or so. In the event of someone not logging out cleanly with the approprate telnet commands, it was easiest to just reboot the switch.
In short: It isn't really dangerous, but it can in certain cases yeld annoying results.
1Awesome. Exactly what I was looking for. – Nicotine – 2016-09-01T14:03:11.690