Good interviewers want you to pass, and aren't just giving you a test of arbitrary programming trivia.
Lip service is certainly paid to 'everyone has to look things up', and doing a quick search won't necessarily count against you, but, IME, the hesitation and doubt that caused you to look things up will. With so little material with which to evaluate a candidate, absolutely everything that doesn't impress them is going to count against you.
This is certainly Google’s philosophy, but our industry doesn’t think with one mind on this.
And as for having so little material - to me this is a sign of a badly designed interview. Almost everyone is weak in one area or another. If your interview only assesses candidates in one way (eg via a coding challenge, or based on a single whiteboard problem) then you are making a decision with insufficient signal. Multifaceted interviews are good interviews.
Plenty of otherwise strong candidates are weak in at least one section of any assessment. And plenty of bad hires will still, for example, know trivia about data structures even though they don’t actually know how to program. Making a hiring decision based on a single metric leaves way too much to chance.
(Source: I’ve done over 400 technical interviews)
> "I'd Google the exact algorithm for X"
This is a fail in the interviewer's book. Read: "Could not produce an algorithm with less than O(n)" or "lacks familiarity with fundamental data structures"