Without producing the requisite 501(c)(3) determination letter, you will not be able to receive the non-profit discount.
This may seem arbitrary, but any discount program such as this has to have qualifiers and terms or it risks the granting of the benefit being perceived as subjective, and that in turns brings the risk of people becoming frustrated and alleging "you did it for them but you didn't do it for me". The next thing you known discrimination is being alleged, and so on.
These kinds of scenarios come up from time to time, and we have tried to be clear about that in our wiki, when we say:
"A 501(c)(3) determination letter is the only documentation that we will accept. If you are a non-profit organization and do not have a determination letter, regardless of the reason, you will be denied free hosting. "
This mean exactly what it says. The 501(c)(3) determination letter is what we have decided to be the qualification to have the free hosting. Without that, we decline to make "one-off" exceptions and grant certain groups the privilege anyway.
Just ask the church for their letter. I see no reason to be concerned about telling them why you are asking for it.
--DreamHost Tech Support