Short answer: The employer still pays the premium but reports it as taxable wages, so any benefit the employee later collects is tax-free. The employee pays a little tax each year on the premium instead of income tax on every disability check.
Disability benefits follow the tax treatment of the premium. When the employer pays the premium and leaves it out of income, benefits are taxable (IRC 105(a)). When the premium is included in the employee’s income, the employee is treated as having paid it and the benefits are excluded (IRC 104(a)(3); IRS Publication 525).
A gross-up design puts the employer-paid premium on the W-2. Some employers also add cash to cover the tax on it. The cost to the employee is tax on a modest premium. The payoff is a full, untaxed benefit when they can least afford a cut.
Run the comparison on take-home pay: a taxable benefit of 60% of salary replaces noticeably less than 60% of what the employee actually lived on. Rev. Rul. 2004-55 lets the employer offer the choice each plan year instead of imposing it on everyone.