Must've been a quiet check-in at the premium area, or the staff don't care much (or just called you forward). Otherwise, I can't believe you used F check-in as a VA WP. Even a SQ KF Gold would (or should) get knocked back from F check-in unless they are flying F. Certainly as a *G the other day, I didn't dare try F check-in and went straight for the J line (as signposted).
J lounge access is a given, as is priority boarding with J (including SQ KF Gold and Star Gold).
Actually I was in MEL when I flew Y MEL/SIN using TK*G (could've used VA G as well but what the hell). When they called boarding they called for First and Business customers first. I stood up because I took Business to mean Business + Star Gold + other qualifying elites. Maybe they really only meant Business Class passengers. I wasn't knocked back, but it was awkward having that green striped boarding pass in a sea of blue, then boarding the 77W and walking through all of Business to get to my seat.
You have to flash the card somewhere, and often (especially in other lounges overseas) they can and may demand to see your qualifying membership card in addition to your boarding pass in order to grant access to lounges.
As for at check-in, again having the card helps and sometimes is demanded. (For example, I've pulled up to Star Alliance Gold desks at check-in, but before formalities even start with the passport, I've been asked to show my Star Alliance Gold status). After this, everything usually smooths out - priority baggage, priority security / immigration access (where applicable - not a gazetted benefit), extra baggage allowance, and so on. Sometimes the desk where you're entitled for priority check-in is a Business desk (or whatever) and hence as long as they verify you are eligible to use the desk, they pretty much mechanically grant you all the other benefits as if you were that class of service (i.e. no real reason why, beyond proving your eligibility, a card is needed to enable all other perks).
Note that preferential seating is not a gazetted benefit for VA Platinum (or Gold) on SQ. Mind you, it's not gazetted for Star Gold either, so as far as seating goes we can only take what we can get (or, in some cases, what you are prepared to pay a fee for)! From what I can tell from experience, entering my *G number on a booking with SQ makes little difference to the seat availability. If the flight is full, almost no chance, but if it isn't, the selection can loosen up closer to departure. Then, your best chance - if there is any - to get the best seat will be at the airport with a polite request to the agent.