I think that it is arguable wether input represents the actual background in a ChIP-seq better than an IgG control, but probably a lot of considerations went into this, so I'll gladly stand corrected :-)
As I see it, then the background might be affected by carry-over as you mention, and more or less systematically distored by the purification method - both locally and in more diffuse ways. Input would not capture this.
On the other hand, the higher DNA yield and number of reads as mentioned will improve statistics, and be a good reason to prefer input over IgG control. However, I think that having both is preferable.