You would be correct in English.
The problem is that Japanese grammar is so radically different, trying to make parallels to English grammar is often futile.
The sentence "Watashi wa nihongo o hanashimasu" means "I speak Japanese", but more literally it means "As for me, I speak Japanese". "Nihongo" is the direct object and hence is followed by "o".
The major difference with "Watashi wa nihongo GA hanasemasu" is that this literally means "As for me, Japanese is/can be spoken".
"Hanasu" meaning "to speak" is turned into "is spoken" "Hanaseru". The passive forms of verbs can also be used to indicated potential, and hence when wanting to say "Can speak Japanese", you'll literally be saying something more like "Japanese can be spoken".
You may also see the sentence structure " Vdic + koto ga dekiru" to mean "Can do something". This is a set expression, and its grammar shouldn't be analyzed extensively.
Suffice it to say, it means literally "I am able to do the act of doing something".
So yep. While English grammar rules very rarely apply to Japanese, other than transitive/intransitive verbs and some other things, the fact that Japanese is a language heavily built around particles (which include wa, ga, o, and many others), and that these particles often don't translate directly into English means that if you try to literally translate a Japanese sentence into English, or analyze the grammar, you'll often end up confused and with even more questions. :)
Lesson 3.2, Wa and Ga