Instrument availability when there is misspecification

A misspecified model can mean that there are no error uncorrelated instruments available. For example, suppose that the generating model is y = a.x^2 + error while the estimated model is y = a.x + error, then as x goes up for any reason, so does the expected error. Thus any causal variable on x also increases the error in estimation as it rises, and any instrument is error correlated. I suppose that this is why instrument exogeneity tests are also known as misspecification tests.