Very difficult to find a form of words for this. As to the meaning, I'm pretty sure your contact is right. "Nominativa" strictly means that the name of the recipient appears in the budget; they are grants earmarked for particular individuals or entities. "Digitadas", in this context, must be a fancy way or saying "asignadas a dedo". That is precisely what gives cause for concern in this area.

For "a dedo", I think arbitrary is the best word to choose. I like "cronyism" or "string-pulling", which were suggested in an earlier question on "a dedo": http://www.proz.com/kudoz/spanish_to_english/other/520724-a_... , but I think they're too colloquial and too explicit here; "arbitrary" was favoured in another question, I think rightly: http://www.proz.com/kudoz/spanish_to_english/government_poli...

"Nominativa" is tricky, because it doesn't really say what it means. At first sight, why should it matter that the recipient is named? Simply because it means there's no open application process; public money is awarded without inviting applications and considering their merits; it's decided in advance who gets it. That lack of openness is what's causing concern and what has led to PP to call for banning them:

"El PP pide eliminar las subvenciones nominativas y garantizar un "uso responsable" del dinero público"
http://www.europapress.es/economia/macroeconomia-00338/notic...

This doc. explains a bit more about them:

"Artículo 65 del Reglamento General de la Ley General.
1.- Son Subvenciones Nominativas aquellas en las que el Objeto, dotación presupuestaria y beneficiario aparecen designados expresamente en el ESTADO DE GASTOS DEL PRESUPUESTO”.
2.- Aquellas Subvenciones cuyo otorgamiento o cuantía venga impuesto a la Administración por una norma de rango legal.
3.- De forma excepcional, aquellas otras Subvenciones en que se acrediten razones de interés público, social, económico o humanitario, u otras debidamente justificadas que dificulten su convocatoria pública."

There you are: no convocatoria pública. It's a closed process; no-one else need apply, or indeed can apply.

So I'd suggest "closed or arbitrary procedure", which I hope is clear enough to be understood but still sufficiently "delicate".