The thinking probably goes that it's only a late payment if the tenant makes an agreement with the landlord, in which case the landlord wouldn't be giving them notice to vacate. If it has gotten that far then it is a missed payment because the tenant couldn't (or didn't try to) reach an agreement in time and it resulted in the tenant breaking the lease. I think many leases include provisions for late payments for this reason, even in states with pro-tenant laws.