Not just applicable to Oboe - this principle affects all woodwind and presumably keyed brass instruments.
I don't tax myself with anxiety over small "sympathetic movement" (which occurs with almost any finger for me except pinkies!)
The main focus I apply is to the most economic movement (distance = time) and the desirability of using "formulae" style thinking to "print" whole fingerings discreetly on the keys. (see advice on the fingering chart I posted a few months back).
Always assume that the most "natural" fingering is the one with no keys depressed and fingers almost or just touching the keys, but sufficiently above the open holes (say max 5mm) as to not affect pitch.
All fingers descend from that neutral state to whatever pattern required (and the unused fingers stay in that neutral state) and retun to the neutral state if not required by the next "overprinted" fingering.
Get the thinking right and the action will be right by default.
Sub-comment: bassoonists even apply this to the R hand thumb!
Christchurch New Zealand
Bassoonist / Teacher / Conductor