As a matter of fact, the chart above is not wrong; it is quite correct. Indeed, histidine can carry a net positive charge, but when unprotonated, i.e. in a charge-neutral state, its aromatic π-system (belonging to the imidazole moiety) can behave like a hydrophobic group, e.g. it can become involved in π-stacking (aka CH-π) interactions. In the 2RS2 NMR structure, for example, HIS83 is δ-protonated and appears to be behaving like a typical hydrophobic residue: it is buried below the protein surface, stacked against several aromatic residues and packed along with several aliphatic ones; it is shielded from solvent by polar and charged residues.
2H95 is a very interesting structure where we see four ε-protonated histidines stack against tryptophans, as well as pack against aliphatic side chains, forming a transmembrane proton channel. The histidines appear to be involved in hydrohobic interactions, and, notably, at the same time form the inner surface of the channel.
Conversely, in the 2NBJ NMR structure, we see HIS56 behaving like a polar amino acid - its (doubly protonated) side chain is involved in hydrogen bonding to the backbone oxygen of a DNA fragment, as well as to a backbone oxygen atom from the protein. Moreover, in the same structure, HIS16 is doubly protonated and solvent exposed, likely interacting with water and contributing to solvation, in stark contrast to HIS83 in the 2RS2 structure, which is monoprotonated and buried in the hydrophobic interior of the protein.
Histidine's pKa can easily be perturbed by its surroundings, e.g. by the surrounding residues in an enzyme active site, which makes it highly functionally versatile, one of the manifestations of its functional and chemical versatility being its ability to behave both as a polar/charged amino acid, as well as a hydrophobic residue; this is the reason histidine is often found in functional sites in proteins, e.g. enzyme active centers.