Why should the salt being used in salting out process be neutral?
"Its [sic] been said" is inadequate contextualization. Many organic solutes are potentially capable of being ionized, especially in aqueous solution. Maintaining aqueous media at a neutral pH will for most solutes minimize this (undesired) effect. For instance, in the following reference (note date and distinguish between what is observational (and thus probably "true") and theoretical (based on what is likely to be incorrect chemistry)), read the last sentence on page 531 over to 532. http://www.jbc.org/content/33/3/531.full.pdf