In this case Google are acting as the mail host and a different set of rules apply to those than Gmail addresses. Your company can specify the same behaviour if they want, but they clearly haven't in your case.My employers use Gmail, albeit the end of our addresses is the company name and '.co.uk'.
That's the address I just tested, so it is definitely dot sensitive for my first and last name.
Gmail addresses may contain dots but the dots are there purely as a presentational item, think the same with capitals. FirstnameSurname@gmail.com is the same as firstnamesurname@gmail.com - it's just easier to read. It's the same address as Firsname.Surname@gmail.com and firstname.surname@gmail.com - if you are unfamilar with these rules then confusion can abound.