blue monday, the stories were undoubtedly true, just wrong
The origin os the stories predated the U2 shoot down by a number of years. I believe you will find stories both here and on the internet and I think the aircraft involved were B45s and in Eisenhower's time. It was potentially less politically embarassing if USAF or CIA personnel were not involved.
You will also find stories of the RB47 penetrations deep into Soviet airspace.
IMHO the Soviets were quite rightly paranoid about western attack, after all every man and his dog had attacked them in 1917-1921, then Germany, an erstwhile ally attacked them, then Patton and others made it equally clear what they would like to do, then the atom spies showed how the west was planning a pre-emptive strike. Mmm