SAY PLEASE!

Say please!
The other day I realised that I had left my bag in the staffroom so I went back to get it and seeing that my seat was taken and I couldn't get my bag myself,asked in a polite voice "Could you pass me my bag?" I couldn't believe my ears when the woman sitting next to it said "Say please!" and the person next to her said "whats the magic word?". I said "I asked you politely" feeling shock and indignation at the request.
My partner informs me that 'please' comes from 'plea' which means to beg. I also have been at a shop with my children where the woman wouldn't serve my children  and berated them for not saying please.I told her that it was a transaction, and while recognising it as a cultural form of politeness, it was no indicator of rudeness if one didn't say it.Moreover, in the second scenario the shopkeeper clearly did not understand that a transaction was taking place ie money (and her livelihood) for an ice cream.If anyone needs to beg then it should be the shopkeeper.
Its one thing for saying please -and indeed 'thank you'- to be a cultural habit, and another for it to be a mandatory request which if not given the goods or services are withheld.
In the Cook Islands and many Polynesian cultures no one says please or thank you-they are mystifyed by its use as to them taking and enjoying the food or whatever is thanks.I believe in New York when ordering food one says "I'll have.........".  No 'please' demands.
Postscript: Scenario: I rudely reached right over them and grabbed my bag.