Basic Strategy defined (in my own words):
Is the proper playing decision based on the player's 2 cards vs the dealer's up card with no further knowledge or information.
In single deck BS there are fine point decisions that can be made based on 2 (and more) card combinations. This is additional to refining BS but not mandatory to learn as part of Basic Strategy.
This is Basic Strategy defined in the Blackjack Glossary on this site:
"Basic strategy. The fundamental playing decisions made by a player when determining the proper play to make given the player's cards. Basic strategy is not based upon the count, but rather upon the total of the player's hand and the dealer's upcard. It can vary based upon the number of decks in use and the specific rules of the game being played. It is determined by which action the player can take which will maximize the player's return based only upon the knowledge gained from the player's hand and the dealer's upcard."
You implied that using Basic Strategy while gaining knowledge from previous played cards would be wrong. Yes..When using knowledge gained from played cards and applying that information you are not using Basic Strategy but altering that decision (if needed) based on information. An example would be: you are playing with one other player at single deck and the dealer asks for insurance. You see your 2 cards and the other player's cards and there are no 10 values cards in either of your hands. It is a correct decision to take insurance at this point. You have information and you are not playing basic strategy.
Basic Strategy decisions have been devised by many knowledgeable people with billions of simulations run. Trust the decisions.
When card counting you have information and will deviate from basic strategy based on information. Trust those numbers not your intuition as the other "author" says.