LMAO! As a person who was a teenager when this song came out, I got a real kick out of the some of the above replies!
Okay - the original German version (because Nena, the band, was German

) was "99 Luft Balloons" - "99 Air Balloons", as stated above.
Nena (same band) then did an English version. "99 Red Balloons". I guess "99 Air Balloons" didn't sound quite as cool! So, not a cover by a different band, just the same band doing it in another language. Plenty of European bands have done this over the years, with only the English version ever hitting the US market.
As for "Luft" meaning red - um .....
Luftwaffe,
Lufthansa ..... I think you get my point. Although, come to think of it, the Red Baron's plane
was red ...... !
And, finally, to answer the original question, yes, it was a Precision. He uses one in the video (which means nothing), but the sound is clearly a Precision - or some very good producing to make it sound like a Precision.