Obviously each case should be dealt with on its own facts to assess the application of GDPR. In the example you give, GDPR may well apply. Some companies may be worried, others may see it as an opportunity.
I know lots of US SaaS companies are embracing GDPR rather than being worried about it. Clearly if you are looking to get business from EU customers but want to argue GDPR doesn’t apply due to the fact you are not strictly speaking targeting EU users then that might present an issue for certain potential EU customers (or maybe they could offer a cost discount because they haven't had to go through a GDPR compliance exercise). On that basis lots of companies outside the EU are pro-actively looking to comply with GDPR.
Arguments over the appropriateness of extra-territoriality applicability are a separate matter of course!