Protein-surface interactions are ubiquitous in both the cellular setting and in modern bioengineering devices, but how such interactions impact protein stability is not well understood. We investigate the folding of the GB1 hairpin peptide in the presence of self-assembled monolayers and graphite like surfaces using replica exchange molecular dynamics simulations. By varying surface hydrophobicity, and decoupling direct protein-surface interactions from water-mediated interactions, we show that surface wettability plays a surprisingly minor role in dictating protein stability. For both the beta-hairpin GB1 and the helical miniprotein TrpCage, adsorption and stability is largely dictated by the nature of the direct chemical interactions between the protein and the surface. Independent of the surface hydrophobicity profile, strong protein-surface interactions destabilize the folded structure while weak interactions stabilize it.