Change of material and influence on stress calculation in analysis

Hello, 

I compared maximum stress of my model in a linear static analysis with different materials. I went from steel to 7075 aluminum (lower youngs modulus and higher cross contraction number). The rest of my model including the load cases stayed the same and i expected the stress to be higher in the case of aluminum because of its lower youngs modulus. But the exact opposite was the case. How can this be explained? 

I did some research and found this quote in a PDF from altair (https://www.altairuniversity.com/wp-content/uploads/2014/02/postproc.pdf) : 'Changing the material will not require rerunning the analysis for stress (in case of linear static analysis) and a decision could be taken just by comparing the maximum stress value with the yield / ultimate strength of the material' 

So i get different stresses in a linear static analysis with different materials, but this quote says an analysis rerun is not required. I am confused. 

I highly appreciate if anyone has an explanation for this. 

Thank you very much, 

Johannes