Meta-analysis Question- sensitivity analysis and heterogeneity testing

Hello all,
I appreciate any insight into this meta-analysis.

This is a meta-analysis on alogliptin efficacy and safety. In the 2nd paragraph of the discussion that make this statement:
Although heterogeneity testing showed a statistically significant dissimilarity in the results of the included studies, sensitivity analysis has shown the stability of the overall odds ratios with the withdrawal of any of the study from the analysis without a significant improvement of the heterogeneity. Thus, the credibility of the results of this meta-analysis did not seem compromised. This is because; when the number of included studies is small and heterogeneity is large, the robustness of the results is best assessed with a sensitivity analysis

What in the world do they mean by "sensitivity analysis has shown the stability of the overall odds ratios with the withdrawal of any of the study from the analysis without a significant improvement of the heterogeneity"

Do they mean when one outlier study is removed the ORs don't change? What are they trying to communicate? Please help!

Citation:
Efficacy of alogliptin in type 2 diabetes treatment: a meta-analysis of randomized
double-blind controlled studies
BMC Endocrine Disorders 2013, 13:9

Here is a link to the article:
http://www.biomedcentral.com/content/pdf/1472-6823-13-9.pdf