I'm not Russian but it's obvious that Russian sentence:
"Кажется, он говорит по-русски." doesn't mean 'He (subject) seems (verb) to speak (infinitive) Russian (direct object of infinitive)'.
There are two verbs that indicate TWO subjects: кажется and говорит.
1) It seems he speaks Russian. 'Wygląda na to, że on mówi po rosyjsku' - I am a subject (or there is some "people"'s subject) and the second part is from my/widely recognized perspective. Wygląda na to or zdaje się mean "It seams" - in English you need to use the dummy subject while in Polish and in Russian we only use the verb for the third person singular (like it :) ) and we use the się/-ся pronoun to indicate impact on the surroundings.
2) He seems to speak Russian. 'On wydaje się mówić po rosyjsku.' He is a subject. It's about his impact on other people. Remember verbs are also about "feelings" not only actions.
They mean the same thing like the passive and active voice. But you use them for different emphasis, like e.g.:
-I wrote a book. (active)
-A book was written by me. (passive)
The same thing but emphasis is different and personally I think that first sentence " feels more natural" :) But it doesn't mean that you can't use second type of grammatical construction, right?
We could use a native speaker's comment for a more accurate description of reality from the Russian point of view. Very often our grammars present the same problems using different tools. I'm courious how they say: "He seems to speak Russian".