Everyone has a hidden creativity and few are express their creativity through pen or pencil and few are with their visibility and preferences. So let's a customer don't want the system fonts (Arial, Verdana, Times New Roman, Georgia etc) and asking for little different font to make his/her website little different by typography.
Don't worry about the requirement and even don't need to convince them to use images or any other options other than Google Web Fonts API. The Google Web Fonts is really beautiful, readable, accessible and open source. Just choose the suitable one and apply on the website, hope your customer will be happy.
