You are responsible for your safety so if you want a buddy check, ask for it. If they aren't willing or you don't feel safe - call the dive. Seriously if at any time you feel pressured to do something you don't like, aren't comfortable with or in a manner that disturbs you, feel free to call the dive. As is said a lot on these forums diving should be fun and if it isn't stop doing it. At worst a buddy check will take 1-2 minutes so what is the big hurry??? The ocean/sea/lake isn't going anywhere in the near future! Another often quoted adage on here is that it is better to be on land/boat wishing you were in the water than in the water wishing you were on land /boat - in other words don't get yourself in to a situation where your safety is at risk.
It is interesting to hear an instructor describe your octo as the buddies problem. Should your primary fail for any reason you can switch to your octo while problem solving it (mine started breathing wet near the start of a dive but still delivered plenty of air so buddy and I surfaced, discussed it, detuned it so no freeflow and continued the dive safely)
I have to say that I started out doing full buddy checks with my buddies (and still will with a new buddy) but after a few dives, you get to know them, their kit and how well they set themselves up so you end up stripping it down to the minimum as per BoulderJohn below (with each of us casting a critical eye over our own gear and theirs).