“Trust the science” has always bothered me for two reasons: 1) science is frequently not black and white and anyone who has done hard science research knows there are plenty of competing opinions among scientists and 2) while scientific facts are facts, we still need to decide on how to act on those facts and that decision making process is most certainly political and subjective in nature.
"The Royal Society's motto 'Nullius in verba' was adopted in its First Charter in 1662. is taken to mean 'take nobody's word for it'. It is an expression of the determination of Fellows to withstand the domination of authority and to verify all statements by an appeal to facts determined by experiment."
It's highly consistent with the statement above and in many ways is consistent with science as it is practiced.
(sorry, couldn't resist)
> The essence of science is to distrust authority and received wisdom
"take nobody's word for it" -> anyone can say anything, that is just a claim, things other than that matter like data, replication, etc.
That is different and superior than a simple, broad, statement to 'distrust'.