Stephen Senn in his 2000 article on meta-analysis shows that there is a clear map from methods to analyze a multi-center RCT to a meta-analysis. I don’t see how ignoring the study level in the hierarchy could be valid.
The meta-analysis of a group of simple clinical trials can, from one point of view, be regarded as isomorphic to a multi-center clinical trial, with ‘group’, ‘trial’, ‘patient’ in the former being replaced by ‘trial’, ‘center’, ‘patient’ in the latter. Both are examples of hierarchical data sets.
The best way to deal with this is to use some of the regression methods mentioned above, that do not ignore the hierarchical structure of the data.
Senn S. The Many Modes of Meta. Drug Information Journal. 2000;34(2):535-549. (link)