The Short Version
The claim is true. Multiple independent, high-authority sources — including NASA, ESA, NSF, and peer-reviewed research — confirm that tardigrades have survived real exposure to outer space conditions. In the 2007 FOTON-M3 mission, tardigrades survived space vacuum for 10 days and even reproduced afterward. Survival is time-limited and reduced under intense solar UV radiation, but the demonstrated capability to survive space exposure is well-established scientific fact.