Personally, I would just shut up about the oil change. (failure to change oil did not make the engine "run out of oil"). I would put oil in the thing and see if it starts. If it does good. If it does not the generator has a three year warranty.
If Cummins tells you that failure to change oil caused the problem (they will not)
then you maybe have a case.
Now to the real question does this generator have a low oil cut off. Cummins has gone to splash technology for lubrication and I find no more mention of low oil cut off in their spec sheet
https://powersuite.cummins.com/PS5/PS5Content/SiteContent/en/Binary_Asset/pdf/Consumer/specsheets/a-1399.pdf
Warranty statement at
http://power.cummins.com/sites/default/files/PGBU-Warranty-Statement.pdf