Correct. "Withholding" is something that companies do when they're legally required to, such as withholding taxes from your salary. When you receive a grant of stock or options, the company is not as far as I'm aware obligated to withhold anything. It's the employee's obligation to pay whatever taxes they owe. I have never heard of a company doing this, and I'm not sure there is any tax provision for it like there is for withholding from salary.

The common practice of immediately selling whatever percent of shares is required to pay taxes on them is something that employees are choosing to do, supported by the trading firms that help implement vesting schedules and stock sales. Employees are allowed to keep all of their shares and pay tax on whatever next interval is required instead, if they wish. One can only follow this practice of selling shares immediately to cover tax if the company's shares are liquid, i.e., the company is a publicly-traded company with an IPO.

I suppose in theory one could receive stock in a private company, and sell shares on the secondary market to cover taxes, but with private companies you can't take it for granted that (i) you'll be allowed to do that at all, or that (ii) there will be a buyer for those shares at all, or at a price you're happy with. With a publicly traded company, it is taken for granted that there's always a buyer for the shares, and at a price that is commonly known and accepted.

Companies do this so that their employees don't get into tax trouble. There were cases when the employees failed to sell the shares needed for taxes and later on the share price crashed and the employees were stuck with big tax bill. Like what I said in my other comment on options, the granted shares are regular income at market value; and if you don't sell enough and later have losses the losses would be capital loss. Unless you have other big gains to offset you can use only $3000 a year to offset your regular income.