"The little tired duck watches TV from the girl's bed."
Translation:Den lille trætte and ser tv fra pigens seng.
"Den lille trætte and kigger tv fra pigens seng" is not accepted. It is only an interpretation but I don't think he just sees the TV , he actively watches it. As you say, Fjernsyn should be good, it is the TV too.
Perhaps the author has chosen a translation among all the possible ones, since this sentence could be said in differently
The end result could be the same, but the two highlight two different things. "Ser tv" means to watch what is being shown, so the duck is actively watching whatever is being shown. "at se på tv'et" is more directly about looking at the tv-set. The cook could be looking at what is being shown but he could also just be looking at the buttons and contemplating how dirty they are.