I agree, mil SIC does not count towards 121 upgrade.
But I wouldn't correct them on that, you might get preferential hiring and FO training placement if they think you can upgrade faster than the CFIs. Of course you'll have to break the news when the time comes, don't let them actually send you to a checkride based on that lol.
For clarity that's for upgrade to 121 PIC, or getting hired as a DEC. You can still get an R-ATP without 1,000 121 hours. You can also get an unrestricted ATP, just can't serve as a 121 CA.