Not true. You need to check local laws. For instance, here is the law in Texas:
"Texas law does not require workers' compensation. However, your customers may require you to carry it."
And in California, if you don't have any employees, you may not be required to have workers' comp (but you should probably carry it anyway if your co-founder is not your spouse):
"My spouse and I are the sole owners of our business. We have no employees. Are we required to obtain workers' compensation coverage?
Generally, coverage for sole owners is optional. You would, however, need to have workers' compensation coverage for any employee you may hire, even if it's just one employee, and even if it’s just temporary employment."
Please update your post to explain that this is based on jurisdiction, and to check local laws.
Also: This is one of many reasons why running a business in Texas is better than running one in California. (Yes, I've run tech companies in both places.)