Rheological characterization of physically crosslinked peptide- and protein-based hydrogels is widely reported in the literature. In this review, we focus on solid injectable hydrogels, which are commonly referred to as 'shear-thinning and rehealing' materials. This class of what sometimes also are called 'yield-stress' materials holds exciting promise for biomedical applications that require well-defined morphological and mechanical properties after delivery to a desired site through a shearing process (e.g., syringe or catheter injection). In addition to the review of recent studies using common rheometric measurements on peptide- and protein-based, physically crosslinked hydrogels, we provide experimentally obtained visual evidence, using a rheo-confocal microscope, of the fracture and subsequent flow of physically crosslinked β-hairpin peptide hydrogels under steady-state shear mimicking commonly conducted experimental conditions using bench-top rheometers. The observed fracture demonstrates that the supposed bulk shear-thinning and rehealing behavior of physical gels can be limited to the yielding of a hydrogel layer close to the shearing surface with the bulk of the hydrogel below experiencing negligible shear. We suggest some measures to be taken while acquiring and interpreting data using bench-top rheometers with a particular focus on physical hydrogels. In particular, the use of confocal-rheometer assembly is intended to inspire studies on yielding behavior of hydrogels perceived as shear-thinning and rehealing materials. A deeper insight into their yielding behavior will lead to the development of yield-stress, injectable, solid biomaterials, and hopefully inspire the design of new shear-thinning and rehealing hydrogels and more thorough physical characterization of such systems. Finally, more examples of bulk fracture in some physical hydrogels based on peptides and proteins are explored in the light of their behavior as yield-stress materials.