I'm assuming it isn't very true, but is it based on a true event? Was there anything like this during the Space Race, where one side over-engineered a solution to a problem that the other side had a very simple solution for?
The Fisher Pen Company had already designed and patented the Space Pen in 1965 before NASA became involved. Paul Fisher saw a need for a pen that could write upside-down, in low pressure, and in temperature extremes.
NASA initially used mechanical pencils. Practically, the problem with pencils is that the lead leaves powder and can break and float around the capsule, where it can be breathed in or, being conductive, short out electronics. The other problem was the uproar over the cost of the pencils procured for Gemini: $128.89 from Houston's Tycam Engineering Manufacturing, Inc. In 1966, Fisher approached NASA, who were initially reluctant. They finally purchased 400 pens for Apollo for $6 each.
The Soviets began using grease pencils in their early flights. In 1969, they purchased 100 pens, plus additional ink cartridges, for use on the Soyuz program.
Sources:
NASA History website
Scientific American, Fact or Fiction?: NASA Spent Millions to Develop a Pen that Would Write in Space, whereas the Soviet Cosmonauts Used a Pencil, 20DEC2006