Teresa Goody, a former SEC official, said Musk "did something inappropriate and caused chaos in the market" in a way that would likely draw scrutiny from investigators.
The board had "met several times over the last week" to discuss going private, the statement said.
"If the market believes that Elon Musk's financing is in place and the chances of a buyout is high, we should see short covering in size, driving Tesla's stock price higher in the short term as short sellers attempt to close out their positions at lower than the $420 takeout price", said Ihor Dusaniwsky, a managing director at S3 Partners.
Musk has downplayed the power of the tweets he launches at all hours to his 22 milion Twitter followers: "My tweets are literally what I'm thinking at the moment, not carefully crafted corporate bs, which is really just banal propaganda", he said in June.
The move to take the company public would remove Musk, who himself has a 20 percent stake, from the public arena - and contentious criticism.
"Only reason why this is not certain is that it's contingent on a shareholder vote", Musk said in one tweet.
But the board offered no further details of the proposal or its funding, sparking new questions about the feasibility of the master gambit Musk revealed in a surprise series of midday tweets on Tuesday.
Lawyers said every word of Musk's tweets will be examined, including why he used words like "considering", to determine whether he might have tried to inflate the stock price to blow out short-selling investors, a longtime foe. "This included discussion as to how being private could better serve Tesla's long-term interests, and also addressed the funding for this to occur".
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Tesla may find it hard to line up banks and investors to lend it large sums. The board said it is now taking the "appropriate next steps" to evaluate the proposal.
One Tesla shareholder said he thought a deal to take Tesla private was doable.
Would Tesla perform better as a private company?
The company also remains unprofitable and going private wouldn't change that.
The company has $2.2 billion in cash and $9.5 billion in debt.
That's debatable. The new tax rules enacted by Congress a year ago could be bad news for Tesla. That's a key reason why Michael Dell chose to list shares of Dell Technologies (DVMT) on Wall Street again after taking the company private in 2013.
Musk seems exhausted of dealing with skeptical Wall Street analysts and short sellers who are trying to profit from declines in the stock. Some might argue that it was improper, and perhaps even illegal, for Musk to make such an announcement on social media because people who follow Elon Musk on Twitter had an unfair advantage over investors who don't.
Is $420 high enough of a price to take Tesla private?