Trouble understanding one specific lyric in a song


I was trying to translate the lyrics of a kids' song for my sister who sent it
to me, but I have trouble understanding one part of the lyrics:

> 「課長 すてきです その一言  
>  ピュアなまでに鈍感」  
>  「社長 すばらしい そのアイディア  
>  民蹴ちらす王のよう」

What does その一言 ピュアなまでに鈍感 in particular mean? I don't even know how to separate
the words here... does it mean that 課長 is so insensitive that he becomes pure?
And what does 一言 stand for? Does it refer to everything he says in general, or
to one thing he said in particular?

The whole song is a pun based on Leonardo Da Vinci's Mona Lisa. The whole
lyrics are [here](http://www.utamap.com/showkasi.php?surl=k-160518-118).  
And the song is [here](https://www.youtube.com/watch?v=j_9EcGdaV6w) (it's from
the NHK).

I have a few other difficulties, like for example why use the English word
"but" in the middle of nowhere? Does it stand for some kind of joke/reference
in Japanese?

Anyway, many thanks for your help! :)




First of all, please keep in mind that the entire lyrics are made of _sarcasm_
rather than _pun_. Everything in the brackets is what this "Mona Lisa The
[Otsubone](https://www.jlect.com/entry/3149/otsubone/)" says. They are
superficially compliments but are actually complaints. (In case you've missed
the implication of お局, please read the link.) A song full of black jokes like
this is certainly not a "kid's song". 一言, as the kanji suggest, refers to one
specific statement. So a translation would look like:

> 課長 すてきです  
>  Chief, you're so wonderful!  
>  その一言 ピュアなまでに鈍感  
>  What you've just said (is) so purely/innocently...insensitive!  
>  (More literally: "... is insensitive to the point it's pure". See the link
> by @broccoliforest if you need grammatical explanation)
>
> 社長 すばらしい  
>  President, how splendid!  
>  そのアイディア 民蹴ちらす王のよう  
>  That idea is like a tyrant wiping out his people!

As always, は has been omitted in those informal sentences.

* * *

> why use the english word "but" in the middle of nowhere?

It's there because the lyricist thought でも looked simply boring and
unimpressive. Is this the first time you read Japanese lyrics? Whether good or
bad, lyrics of Japanese pop songs often have English words or phrases with no
particular reason other than "they sound nice".

