Garden shed base - lay concrete directly on the grass?

your builder is right, laying concrete onto the lawn will be fine, the shed walls weigh nothing, if you aren't storing heavy weighty items (vehicles )on the floor there is still no weight.

The concrete will need mesh in it and you will have to expect the base to sink due to grass rotting and the soil compacting........so what! it's only a shed to keep the lawnmower and garden tools dry.

Use railway sleepers and just level them. easy and fast and will last.

The suggestion the builders gave is the cheapest option, you shouldnt have a problem as its only a shed going on it, if you were driving on it that may be different, providing your lawn areas not a soft bog and you dont skimp on thickness it shouldnt crack or break up