Some people use HLM to mean regressions where one set of parameter's are nested inside another. Another term for this is multiway analysis. Others mean a specialized form of linear regression where variables are added in blocks and a F test tells if you have added explanatory power by adding them. It would help commentators if you explained which you meant by HLM (or something entirely different).
Deviance statistics in the first form of HLM I noted are used to determine if one nested model is better than another. Is that what you meant? If your mentor did a disertation on them, wouldn't one of his disertation committee members have the raw data? Or maybe the IRB board he had to submit his proposal to?
You can run the correlation/covariance matrix with SEM. HLM uses weighted least squares to do the calculations and I would think it would have to have raw data to do that (although that may not be the case). I have never seen the correlation matrix used with HLM. It is true that the results of HLM and SEM time series methods are similar. But that does not mean the way the results are calculated are.