I meant to mention - as hokie66 said above, the whole reason for the bridging, is to ensure that the purlin deflects vertically under ALL types of loading.
If the bridging does not keep the purlin vertical, the deflection distortion is a torsional rotation (due to the fact that the purlin is not axisymetric such as an I section) with a very large reduction in the (effective) I & Z value of the purlin, with a consequent reduction in load carrying capacity. A tie rod cannot develop this type of torsional restraint.
Essentially, bridging is also req'd for C sections but for a different reason. If the C is loaded by the sheeting on the top flange, the loading is (generally) directed thru the neutral axis & NOT thru the shear centre of the C section. The load mutiplied by the distance to the shear centre, will create a torsional moment that will result in a rotation of the C section (under loading). This rotation will result in a reduction in the effective I & Z values.
All of the above conclusions, have been verified by both theoretical studies & testing of 'real life' structures - usually by purlin manufacturers.