High-precision knowledge of electromagnetic form factors of nuclei is an important current activity in nuclear and atomic physics. Such precision mandates that effects of the nonzero spatial extent of the constituent nucleons be treated carefully. A series of simple, Poincaré-invariant, composite-proton models that respect the Ward-Takahashi identity and in which quarks are confined are used to study such effects. All of the models display a general theorem showing how the medium modification of proton structure must occur. Combining this result with lattice QCD calculations leads to a conclusion that a bound proton must be larger than a free one.