IS this structure correct???

[Anthony1000]

Dear folks,
Consider the following sentences:

1. Buying that car, he dug himself into a hole.
2. By buying that car he dug himself into a hole*.

1. Opening that restaurant, he makes lots of money.
2. By opening that restaurant he makes lots of money*.

I heard from a colleague that the 2nd structure is wrong. He argued that in sentences like this adding "by" to the beginning of the sentence makes the structure ill-formed!!!
Is that true?
Please let me know. Thanks in advance.
Anthony

[Tdol]

There's nothing wrong with the use of 'by', though why no comma?