I did ask around at another site (www.foldingcyclist.com; hope I won't get my hand smacked for mentioning a similar site) and asked the site owner about Picnik bikes. His response:
This was most likely a private label bike. It is a common "U-frame" folding bike design from the 1970's. The frame was most probably made in Yugoslavia and imported to Italy and fitted with Italian parts - handlebars, seat, etc. While I've never heard of the "Picnik" brand, there are literally dozens of similar private label bikes whose names are ones I've never heard of. One of the more prominent Italian brands, Bianchi also imported a similar frame.So the Picnik is no real picnic. Still love it, though.