To add to DavRob's otherwise excellent answer:
Even leaving aside out-of-universe proof (e.g. articles discussing the crossover) mentioned by DavRob, the answer is a qualified "yes" based on overwhelming circumstantial evidence. To be more specific:
No, there is no in-universe canon statement unequivocally stating that the ET-looking aliens in the movie are the same species as the aliens living on Brodo Asogi planet whose Senator is Grebleips.No, there is no in-universe canon statement unequivocally stating that the ET-looking aliens in the movie are the same species as the aliens living on Brodo Asogi planet whose Senator is Grebleips.
Such a statement can not possibly exist as it would likely open both Lucas's empire and Spielbergs into possible legal/financial complications - a mere homage/gag is not worth the trouble for their money making machines.
However, the circumstantial evidence is overwhelming enough that, had this sort of evidence been presented in a court case, I would have been fully convinced of the identity matchHowever, the circumstantial evidence is overwhelming enough that, had this sort of evidence been presented in a court case, I would have been fully convinced of the identity match.
To restate the above as an analogy:
facial identification (which, obviously, is a LOT less distinct between individual humans than between different species) is considered a fully reliable evidence in modern legal system. Being picked from a lineup of almost-identically looking humans is enough of an evidence to be convicted for a crime
So why is being picked out of a lineup of very distinct looking species NOT convincing enough for you given the breath of other corroborating circumstantial evidence presented both in my original answer, AND in DavRob's answer above?
What your doubts seem to be is a legal equivalent of: "yes, I know that the defendant's face looks 100% like one on the VCR tabe depicting the crime, I know that his name matches the name spoken by the accomplice and overheard by witnesses, and I know that he was previously overheard to be planning a similar crime. BUT, since there is no DNA evidence, I will assume that the crime was commted by evil doppelganger and vote to acquit".
By the way, another circumstantial evidence NOT listed by DavRob:
- based on everything you know about US IP system, is it remotely possible that a major motion picture could use a likeness of an iconic distinct looking character from another major motion picture without a high profile IP lawsuit, unless there was an explicit OK from both franchises?