By "natural protein intake" they are referring to normal dietary protein intake, in contrast to amino acid supplements given as protein substitutes for people with disorders related to protein/amino acid metabolism. See for example from Wikipedia:
Supplementary "protein substitute" formulas are typically prescribed for people PKU (starting in infancy) to provide the amino acids and other necessary nutrients that would otherwise be lacking in a low-phenylalanine diet.
Some other sources where this phrasing is used:
Evans, M., Truby, H., & Boneh, A. (2017). The relationship between dietary intake, growth and body composition in Phenylketonuria. Molecular genetics and metabolism, 122(1-2), 36-42.
Hoeksma, M., Van Rijn, M., Verkerk, P. H., Bosch, A. M., Mulder, M. F., de Klerk, J. B., ... & van Spronsen, F. J. (2005). The intake of total protein, natural protein and protein substitute and growth of height and head circumference in Dutch infants with phenylketonuria. Journal of Inherited Metabolic Disease: Official Journal of the Society for the Study of Inborn Errors of Metabolism, 28(6), 845-854.
Huemer, M., Huemer, C., Möslinger, D., Huter, D., & Stöckler-Ipsiroglu, S. (2007). Growth and body composition in children with classical phenylketonuria: results in 34 patients and review of the literature. Journal of inherited metabolic disease, 30(5), 694-699.