Proton bunches with maximum energies between 12 and 22 MeV were emitted from submicrometer-thin plastic foils upon irradiation by laser pulses with peak intensity of 4×10^{20}W/cm^{2}. The images of the protons by a magnetic quadrupole doublet on a screen remained consistently larger by a factor of 10 compared to expectations drawn from the ultralow transverse emittance values reported for thick foil targets. Analytic estimates and particle-in-cell simulations attribute this drastically increased emittance to formerly excluded Coulomb collisions between charged particles. The presence of carbon ions and significant transparency likely play a decisive role. This observation is highly relevant because such thin, partially transparent foils are considered ideal for optimizing maximum proton energies.