Book and Greibach (V. Book, Ronald & A. Greibach, Sheila. (1970). Quasi-realtime languages. Theory of Computing Systems. 4. 97-111. 10.1007/BF01705890.) prove that non-deterministic linear time Turing machines are equivalent to quasi-real-time such machines.
The authors say: " For deterministic machines, linear time is strictly more powerful than real-time; here we show that for nondeterministic machines linear time and real-time have the same power. " However, they do not cite or prove the claim that linear time deterministic machines are more expressive than realtime deterministic such machines.