You are correct, my lawyer confirmed similar message last month.
It is much better to stay on Payroll on LOA. In other words, it is ok to get $0 paycheck as long as you are in their book. You are still the employee of the company, but you are taking leave of absence due to personal needs (such as family reason, kid is really sick, planning for marriage, taking 6 months honeymoon or whatever). If you have EAD card, while on LOA term, my lawyer advised that it is COMPLETELY OK to work for other employers, even for jobs that are not in the same job description. At the end of LOA term, there is an expected date where you are need to return to active duty in the company. Hopefully you get 485 approval prior to the LOA ending date.
This is a good strategy to pass beyond 180 days if one think that he/she may get cut. My lawyer advised me to count 180 days from ND, not RD (for safety reason).