I thought, that televidi more or less requires an object, that identifies, what you are watching in tv. Post la laboro li televidas futbalmatĉon. Furthermore if you don't specify the program, you use rigardi, Post la laboro li rigardas televidon. Note, that televido means, what is sent, broadcast. If you write Post la laboro li rigardas televidilon, he stares at the tv set after the work!
Vortaro.net defines "televidi" as "Rigardi televidan programon." It also defines "televidilo" as "Aparato por televidi," using "televidi" without an object.
reta-vortaro.de defines it simply as "Spekti televidon", with several examples using the word without an object.
I'm not sure where you learned not to use "televidi" without an object, but it sounds like it's acceptable to do so.