Yes, but it can be countered by pinning "random-script-from-the-internet.sh" to the untrusted environment. The fork/exec inside bash (or whatever bash is using now) should take care or that, or the kernel itself which is probably a better option. bash + ls -> trusted because ls is in some way marked as trusted, bash + random-script -> untrusted, possibly by default.

Well it makes no sense to worry about side channel attacks if you don't have isolation in the first place, so there is an implicit assumption that you have a sandboxing layer like VM/container/browser (or the built in unix user separation) which don't care about terminals or X11 (usually a separate X server is used which is running inside the sandbox context).