"Sometimes, it is not super fun to run a public company. The exec departure news at Tesla was way overstated," CEO Elon Musk (@elonmusk) tweeted on Friday.

Overstated? Friday's surprise news that two senior engineers had left Tesla Motors (Nasdaq: TSLA) as the company prepares to put its long-awaited Model S sedan into production certainly had an impact, as shares of the Silicon Valley automaker fell 19% on the session.

Coming on a day when the Dow Jones Industrial Average (INDEX: ^DJI) was down just 0.39%, that was a dramatic drop. Tesla's official line  initially was that the engineers' departures were no big deal. The two engineers left for personal reasons, a spokesman said, and the Model S is essentially done anyway. 

But the details -- specifically, who these guys are, and the timing of their departures -- raise some challenging questions.

Appearances matter, and this looks pretty bad
The point that roiled the markets is that these guys weren't just part of the crew. Peter Rawlinson was Tesla's Chief Engineer, and Nick Sampson supervised Tesla's "vehicle and chassis engineering," according to the company. It's a pretty good bet that these two men know more about the Model S -- the tiny nuances of its design and construction -- than just about anyone.

For them to be leaving Tesla as the Model S -- their baby -- is moving through its last phase of development is not trivial; It's a big, big deal. Sure, the car is (presumably) mostly done, but now's the time when the last details get corrected, the last squeaks and rattles get eliminated, and, hugely, the car is prepared for its official U.S. government crash tests.

Why is that huge? The kerfuffle that has embroiled General Motors (NYSE: GM) since its Chevy Volt's battery packs caught fire days after a crash test has ensured that all vehicles with lithium-ion batteries will be getting close scrutiny for a while, especially after side-impact tests. Tesla has long promised that the Model S will be among the safest cars on the road, with a top crash-protection rating. With thousands of preorders already in hand, the company needs to deliver on those promises.

In fact, delivering on the Model S's promises is (or should be) the company's absolute most important goal at the moment. One would think that Rawlinson, Sampson, and all of Tesla's senior engineers would be working seven days a week right now to ensure that Tesla delivers on that crash test -- and on all of the other very high expectations that surround this car. Instead, they're gone.

Meanwhile, Musk said in a statement that a former Daimler engineer and an executive from Volkswagen were hired to step in and help shepherd the Model S through the last pre-production stages and to market. That doesn't quite jibe with the PR department's suggestion that Rawlinson's role in the Model S's development was over.

What's really going on here?

Damage control is underway, but is the damage done?
To its credit, after its dismissive initial response, Tesla's PR crew is now moving aggressively to get out in front of this story. The company has scheduled a media conference call for 8 am (Eastern) on Tuesday in which "members of the senior management team" will discuss the departures and take questions from the media.

But what can they say? I expect Tesla to stick with its story, to say that these departures weren't disruptive to the Model S program, and that everything remains on track for the Model S's launch later this year.

However, the timing of these departures certainly suggests that something has gone wrong with the Model S program. Does the car not live up to internal expectations? Is there a potential safety problem? Did a key deadline get missed? What's the real story?

This is Tesla's first real PR crisis. We'll learn a lot from the company's response.

Your humble Fool will be on that call, and will have more details for you on Tuesday as events warrant. Stay tuned.