Can RSUs be settled with parent company stock instead of stock of the employer/subsidiary?

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Yes.  See Treasury Regulations §1.83-6(d) and §1.1032-3:  For U.S. federal income tax purposes: 

Parent is treated as contributing its own stock to Sub and the amount of the capital contribution will be equal to the FMV of the stock on the date the RSUs vest.  There will be no gain or loss recognized by the Parent on the deemed contribution (but there is an increase in the Parent’s basis in Sub’s stock by the FMV of Parent stock deemed contributed when the RSUs vest).  Also, there is no compensation deduction for Parent since it is not the employer receiving the services.

Sub is deemed to have purchased the Parent's stock for its FMV at the time the RSUs are vested.  Then, Sub is treated as immediately transferring the Parent stock to employees to settle the RSUs with the FMV of the stock at the time the RSUs are vested being the amount of the compensation paid to the employees.  As the entity receiving the services from the employee, Sub is generally entitled to the compensation deduction under 83(h) (deductions equals the amount recognized as income by the employee i.e., FMV at vesting).

Check with accountants on accounting treatment at it may be different depending on agreements, etc. and also if foreign entities involved.