Well, this was unexpected. They tested and tested, said the starter tests good. They replaced the battery and tried it a couple days of sitting and no issues. I picked it up today and so far it seemed fine.
As to the initial battery test, I was there, they hooked a battery test device up and it did something for a minute or two. The cables however were WAY too small to carry a full cranking load, so not sure exactly what it tests.
Time will tell if they got it right. It's a pretty trustworthy shop indeed if not honest they would have told me I needed a starter and a battery). Not that honest = always right of course.
Maybe it's time for a AAA subscription.