Can VAT be avoided on Direct Mail

I work with a local charity and wonder whether the following could lead to situation where VAT could be avoided on postage (and indeed other VATable costs).

assume i am writing an appeal letter, this will be zero-vated.

however using one of the downstream access mail providers would mean that the VAT has to be charged on the postage element.

Could the printing and mailing company not charge a very high price for the appeal letter (which will unoficially incorporate the cost of the postage), and then provide the postage Free of Charge to the charity.

The printer would claim back the VAT on the printing and postage, but would be able to invoice the charity the entire amount at zero vat

Just a thought and would welcome some informed feedback

thanks