Supplier want's to deliver saturated shed, should that be acceptable ?

[Harry Bloomfield]

Before being put out in the rain.

It could get wet, out in the rain!

 

[Why Not Indeed]

wooden base that itself is resting on weed membrane directly on the soil,

If that's a permeable membrane the base will absorb moisture from the soil, and then rot.
If it's a non-permeable membrane, you want to make sure there's not a way for rain to get on top of the membrane as your bearers will be sat in puddles that take a long time go to away, and then rot.

 

[johnny2007]

Perhaps you should have gone for a plastic one, like wot I have got!
Well, it will never rot.

They become brittle and disintegrate in the sun.

 

[JBR]

They become brittle and disintegrate in the sun.

We've had the shed for 23 years, though apart from the roof the rest of it doesn't see much sun. No signs of any deterioration.