why credit card rejected in Europe store?

This happened to me many times in the last few years, but I can never figure it out. Before going abroad, I follow process

 

1. I called the credit card company and left a travel notes.
2. yesterday a store in London denied the card.
3. I called the credit card company, she said:
  3a. yes, she sees the travel notes.
  3b. she said the credit card company never received any transaction request.
  3c. she said the credit card is not debt card, thus there is no need to provide pin at a store making "purchase".
  3d. only cash in advance needs pin code.
4. I know in the past, my own experience the store purchase requires pin code, for  example in sweden. 
5.  I know in the past, my own experience the store purchase did no require pin code.
6.  I know in the past, my own experience the cash advance requires pin code.

Item 3d agrees with 6, but that item 3c does not agree 4 and 5.  This is a mystery to me, can anyone know the answer?