Muilenburg joked in reply: "We might pick up the one that's out there [Musk's Tesla Roadster and its dummy driver, Starman] and bring it back: 'Look what we found!'"
Inroads made in the last couple of years have fueled the space race for the modern era, not the least of which Elon Musk's Falcon Heavy liftoff and subsequent landing - not to mention a little side of showboating when he launched a Tesla Roadster in space, making it the world's highest-mileage auto ever, and it's still going.
The budding rivalry between the companies is anything but playful, however.
Boeing has been making spacecraft since the 60s, and it is only under Muilenburg, that the company started investing much more in space exploration.
And now, Boeing is also working on an experimental reusable rocket called the Phantom Express in collaboration with the US Defense Advanced Research Projects Agency (DARPA). Then there's the support from Boeing's venture-capital arm for an Australian maker of nanosatellites.
With SpaceX delivering satellites into orbit and launching resupply missions for the International Space Station on a regular basis - not to mention sending a vehicle into an orbit around the Sun just for fun - it's easy to forget that the company is still in startup mode. Both companies are behind schedule as they race to begin flights to the International Space Station before Nasa runs out of purchased seats aboard Soyuz craft at the end of 2019.
Observers of the U.S. space programme might add that consistency in direction would also be a plus: NASA has been directed to go to the Moon, then Mars, then an asteroid and finally back to the Moon again over a succession of United States administrations. SpaceX is assembling tools for an enormous rocket nicknamed the BFR. And Muilenburg thinks Nasa should take the lead and leave industry to focus on commercializing space travel closer to Earth. SpaceX has basically made that a reality. In fact, he said, he's "hopeful" it will happen within a decade.