Most tech support agents have no clue what they are doing, they read off of a script they need to use before they give out any answers ... in your case the card you had on file might of had a caching issue which is why when you remove them and add them back on they reset and re-cache everything ...
I used to spend about 5 hours a day taking payments over the phone when I was managing a storage facility, the one thing that we do when a card is not going through is remove it and add it back without having to think about it ...
Microsoft has a bunch of incompetent idiots for tech support and the probably only get paid min wage to do all that work and if they don't it is outsourced so the quality of tech support is way below average which average in the States is horrible ....