"When Portuguese accompany their fado songs (although they may sometimes use the Spanish guitar) they always use the Portuguese guitar"
Eh? How do you reconcile sometimes with always? I thought the terms contradicted each other.
Make up your mind.

Guitar was often used as a generic term for a plucked instrument. A Spanish guitar and a Portuguese one are very different beasts. Their use has NOTHING to do with the name. A couple of hundred years ago those instruments abounded and were used in low-dives, where the music that became fado evolved. Availalbility dictated their use, not patriotic notions.
Am I wrong, or is the Portuguese guitar not really used for other genres of Portuguese music?
Should the Portuguese be concerned because their instrument originated from English guitars?

Now, as for the English guitar, take a look at this:
http://www.standingstones.com/engguit.html

"This instrument is vastly different from the gut-strung guitar, and was actually a revival of the cittern. Although not the kind of instrument I have been concerned with in this book, a brief discussion of it is necessary due to the large amount of music for it from the mid-eighteenth century, the title pages of which all say, either for 'guitar or 'guittar'. Hence, unless one is able to distinguish which music is for the 'English' guitar and which is for the Spanish guitar, much confusion can result.

The English guitar was known in France as the cistre or guittare allemande (indicating its German origin), and in Italy as the cetra. Italian musicians apparently introduced and started the fashion for the instrument in England. The earliest music for it in England is Pasqualinide Marzi's Six sonatas for the cetra or Kitara ... (c. 1740; copy in London, British Library). It soon, however, became known simply as the 'guittar'."

So, an instrument of probable German origin, popularised by Italian musicians, should be a national instrument because of it's name?
Sorry, but the banjo, guitar, mandolin, Irish bouzouki and electric guitar have just as much claim to the title!!
Just look at the ammount of guitarists from England who pioneered and developed electric guitar playing.