First off, learners need to be very careful when analyzing grammar in song lyrics. Lyricists will often tweak the wording of a lyric to better fit a song’s rhythm or rhyming scheme, so just because something is crooned in a song doesn’t mean it reflects the way people would speak or write.
Secondly, you’ve correctly pointed out that sentences can be ambiguous. If I say:
I like to brush my teeth three times a day.
that can mean I enjoy brushing my teeth, or it can mean I’ve decided that three times a day is good for my oral hygiene, whether or I hope to enjoy the act or not. There is no real way to tell. Moreover, the same problem may exist even if we reword the sentence. This sentence is equally ambiguous:
I like brushing my teeth three times a day.
So, there’s no truly reliable way to tell if “I like to be in America” refers to a state of being or a state of longing. It could mean either or it could mean both – especially when it’s sung rather than explained.