University asks not to promote other university's research
The only reason why you should not promote another university's research should lie in science itself.

(fell free to add more examples!)

Acceptable reasons:


Severe scientific misconduct by the other university (made up data)
Their results are too weak and do not support their conclusions
Their research is done incorrectly (bad methods, etc.)
...


Not acceptable:


Your professor does not like their professor
They got their project funded but you did not
They are more advanced on the topic than you
...