Eye of the beholder: Observer reference frame bias in Hickson-like compact groups of galaxies

[Abridged] We investigate how the identification of Hickson-like CGs depends on the observer's reference frame, quantifying how frequently the same system would be recognised from different vantage points. Using a mock lightcone built from the Millennium I Simulation plus a semi-analytic model of galaxy formation, we identified 7709 CGs when applying the standard Hickson-like criteria. For each CG, we placed 1000 random observers on a surrounding sphere and reapplied the velocity and compactness requirements to test recoverability. We also examined the variation of population and local isolation. The velocity concordance criterion shows modest sensitivity to the observer's location: 10% of CGs fail for some observers, typically groups with members with high peculiar velocities (>1000 km/s). The compactness requirement is far more fragile, as 44% of CGs are missed by most observers, and these systems are very elongated or are chance alignments in real space. Tightening selection limits reduces this dependence. Lowering the surface brightness threshold to $\mu \leq 23 \ mag/arcsec^2$ reduces the compactness dependence to 16%, while reducing the velocity limit to $\Delta V\leq 250 \ km/s$ lowers velocity-driven failures to less than 4%. Applying both cuts simultaneously yields up to 84% observer-independent groups, although with a substantially smaller sample. Population and isolation are affected by bright interlopers seen from different directions. While such interlopers are common, they have only a minor effect on the compactness and velocity concordance criteria; however, the local isolation is commonly broken. Observer frame effects, dominated by the compactness criterion, can significantly bias Hickson-like CG samples. However, adjusting surface brightness and velocity difference thresholds allows users to balance the physical reliability according to their specific scientific goals.