Piano has very distinct timbre for each note - there are many people that think they have perfect pitch but only really just learned the timbre for each note on piano and wouldn't be able to identify pitches of puretones for instance.
However for those of us that drift, I think it's likely that we recognized notes by both timbre and pitch, but although now that our pitch recognition has started drifting, we can still identify by timbre.
Absolute pitch is often described as a disadvantage for aural skills as it's often used as a crutch in place of properly identifying intervals and function. I know that when I went through aural skills, I would identify the notes before identifying the interval and draw a conclusion on the interval based on what notes they are rather than hearing them for what they are. Which makes it very difficult for me to pick out vocal harmonies, I'm terrible at picking out vocal pitch and as a result I have to deconstruct notes in my head to figure out intervals when people sing in harmony.
Using your language metaphor, it would be like if you immediately knew what a word in Russian meant in English but didn't actually understand Russian. You'd be linking together words to infer meaning but grammar might not make any sense and you wouldn't be able to speak Russian. (Bad analogy, but hey, that's how analogies are right? :P)
Definitely sympathize on the drift though. It's annoying when I assume I still recognize notes properly but then realize I'm off.
I think it's fine to expect engineers to know graph algorithms in terms of what they do and when to use them, but knowing how to implement them on the spot on a whiteboard is stupid. This one company had an interesting problem that I identified quickly as an application of A* with some interesting edge cases on top. Working through those cases and coming up with the heuristic was clearly the main point of the interview, or so I thought. The interviewer asked me to write out A* on the whiteboard...