Elon Musk's big personality won't exacerbate Tesla's possible punishment by the Securities and Exchange Commission, former SEC Chair Harvey Pitt told CNBC on Wednesday.

"The good thing about the SEC and its very hard-working staff is they are very much determined to do what they believe justice requires. They are not going to take positions for public approval or because a person has a personality," Pitt said on "Power Lunch."

Pitt's comments come after a New York Times report that the SEC has served Tesla with a subpoena following Musk's tweet that he was considering taking the company private and had the necessary funding.

Musk's statement that he had the "funding secured" has come under particular scrutiny, as it may have violated an SEC rule requiring that public statements made by company executives be true. He explained earlier this week that the Saudi Arabia sovereign wealth fund had expressed interest in taking Tesla private.

This isn't the first time Musk has come under fire for recent erratic behavior. In July, he took to Twitter to call a British cave diver who assisted in the rescue of a Thai boys soccer team players as a "pedo guy." During Tesla's first-quarter earnings call in May, Musk dissed analysts, cutting off Sanford Bernstein's Toni Sacconaghi because of what he called a "boring, bonehead" question. Musk later apologized to spelunker Vernon Unsworth and Sacconaghi for his comments.

Pitt agreed Musk is a visionary entrepreneur, but said his tweets complicate already troubling realities in Tesla's business.

"Well I think he is a man of great vision, there is no question about this. And the car's he's actually produced are quite spectacular. The difficulty is he doesn't seem able to produce them sufficiently to meet the demand he's created and he is burning cash at incredible levels," Pitt said.

"Those are very serious deficiencies and that's why his tweets just made the whole situation much more complex," he added.

Pitt previously warned that Musk could face civil and criminal penalties if it is found that he didn't secure financing at the time of his tweet, which Pitt said is still "the most critical factor."

"I think the most critical factor is did he have a legally enforceable right or agreement to have funding provided for the transaction? It appears from his own subsequent posting that he did not," Pitt said.

Shares of Tesla closed down 2.6 percent Tuesday at $338.69.

Tesla did not immediately respond to a request for comment.