A Hagedorn alternative to inflation?

Robert Brandenberger, Ali Nayeri, and Cumrun Vafa argue that a stringy phase of cosmology dominated by strings near the Hagedorn temperature is an alternative to inflation.

More precisely, their calculation suggests that one can obtain a scale-invariant spectrum by assuming that the temperature was near the Hagedorn temperature in the past - and the environment was dominated by a long, strongly excited string. Moreover, the amplitude of fluctuations from the scale-invariant spectrum is suppressed by the fraction "(l_{Planck} / l_{string})^4", and this insight implies a consistent picture for "l_{string}" being roughly 1,000 times longer than "l_{Planck}", with "g_{string}" being the inverse quantity 0.001.

That's an exciting statement. You can have two possible negative reactions; it is either wrong or equivalent to inflation (much like the good features of the ekpyrotic Universe may be argued to be equivalent to inflation). Assuming that the calculated scale-invariance is correct, which I have only checked partially so far, the second possible answer is pretty interesting. How can this picture be equivalent to inflation? In fact, how is the usual causality argument that implies that the temperature should not be isotropic evaded?