Es Que No Entender Esta Canción Es Inevitable

One of the most infamous differences between English and Spanish is the double-negative-that-really-means-single-negative: unacceptable in English, necessary in Spanish.  For example, "I don't have anything" in Spanish is "No tengo nada," which literally translates to "I don't have nothing."  There is no counterpart to anything in Spanish that is separate from the "negative" nada (nothing), which makes words like nada and nunca used the way English speakers us anything and ever as well as nothing and never.

Keeping this in mind, I bring to your attention Exhibit A: the song "Inevitable" by Dulce María.  The full lyrics to the song make it apparent that the singer is, in fact, falling in love with the addressee.  Lyrics such as "te quiero amar" ("I want to love you") and "Tu boca dice ven, tus besos dicen ven, Tus ojos me derriten, baby" ("Your mouth says come, your kisses say come, your eyes melt me, baby").

This is why one line in the chorus is particularly and frustratingly confusing to me:

"Es que no enamorarme de ti es inevitable"

Which translates to:

"(The thing is that) me not falling in love with you is inevitable"

Personally, this lyric gets under my skin.  I am used to "No tengo nada" ("I don't have anything") and "No lo haré nunca," ("I won't ever do it"), but "Me falling in love with you is inevitable" should be "Enamorarme de ti es inevitable."  Now, if inevitable (same spelling and meaning though different pronunciation in English) is considered a "negative" word in Spanish like nada or nunca, this might seem to fit under the Spanish double-negative-that-really-means-single-negative safety, making the actual translation "Me falling in love with you is inevitable," which is what makes sense in the context of the song.  However, similar sentences with this same structure would mean exactly the opposite because they leave the double negative meaning intact: "Es imposible no hacerlo" means "It's impossible not to do it," whereas following the logic of the "inevitable" lyric it should mean "It's impossible to do it."

The kicker is, in another context, the same lyric can be understood to mean "Me falling in love with you is not inevitable," i.e. "I am never/not necessarily going to fall in love with you."  Although native Spanish-speakers (at least the ones I have consulted) know which meaning to infer, it is by the context, and the interpretation could go either way to the native ear depending on that context.  But in this song, the singer NOT falling in love inevitably just doesn't make sense.  

So my questions are: is inevitable a "negative" word like nada or nunca?  Is imposible?  Is context the sole determiner here, or is this actually just lazy grammar?  Could "No hacerlo es imposible" mean "Doing it is impossible," or "No hacerlo es inevitable" mean "Doing it is inevitable," as opposed to their negative counterparts?  Native speakers and non-native speakers -- what are your thoughts on this subject?