That's mostly correct, in fact there was a lawsuit to determine who could call themselves Tesla's "Founders" and the outcome was that Eberhard, Musk, Tarpenning, JB Straubel, and Ian Wright all agreed to be Co-Founders. [1]
TeslaRumors has a much more descriptive version of events that summarizes how it all came about:
So in 2003, JB Straub phoned Musk and invited him to meet so that they could discuss space and electric car related interests.
[...]
During their lunch meeting, Straubel mentioned a company called AC propulsion that had developed a prototype electric sports car using a gasoline-powered kit car.
[...]
When Musk visited AC Propulsion, he not only was demo’d the car, he also got to drive it. He was impressed. He tried to for months to convince AC Propulsion to commercialize the electric vehicle and even asked them to make one for him, but they had no interest in doing so. Instead, Tom Gage, the president of AC Propulsion introduced Musk and Straubel to another team that shared the same interest so that they together they could increase their potential for success in commercializing an electric vehicle. The other team included Martin Eberhard, Marc Tarpenning and Ian Wright.
[...]
Fortunately, one day Wright's neighbor, Martin Eberhard, started to chat about having just incorporated a electric car manufacturing company. Wright thought the idea was far-fetched but did the neighborly thing and offered to take a look at Eberhard’s business plan.
[...]
They joined forces that year and formed Tesla Motors Inc. Straubel became CTO, Eberhard became CEO, Marc Tarpenning became CFO, and Elon Musk became the Chairman and the Head of Product Design. Ian Wright became Tesla Motors’ first employee as VP of Vehicle Development. Musk provided the majority of funds for the startup with $7.5 million of his own personal cash in the first round of capital investment as well as contributing to subsequent rounds. [2]
1 - http://news.cnet.com/8301-11128_3-10357665-54.html
2 - http://teslarumors.com/HowTeslaBegan
