  We present an interpretation of zero field diffuse neutron scattering and of
high field magnetisation data at very low temperature in the frustrated
pyrochlore system Tb2Ti2O7. This material has antiferromagnetic exchange
interactions and it is expected to have Ising character at low temperature.
Contrary to expectations, it shows no magnetic ordering down to 0.05\,K, being
thus labelled a "spin liquid". However, the ground state in Tb2Ti2O7 is not a
mere fluctuating moment paramagnet but, as demonstrated by very recent
experiments, a state where the electronic degrees of freedom are hybridised
with the phononic variables in an unconventional way. We show here that, by
approximating this complex and still unraveled electron-phonon interaction by a
dynamic Jahn-Teller coupling, one can account rather well for the diffuse
neutron scattering and the low temperature isothermal magnetisation. We discuss
the shortcomings of this picture which arise mainly from the fact that the
singlet electronic mean field ground state of the model fails to reproduce the
observed strong intensity of the elastic and quasi-elastic neutron scattering.
