I thought that stranger anxiety was a perfectly normal stage for kids. I'm suprised your doctor would tell you to put her in daycare to get her to stop this behaviour, especially considering that daycare wouldn't even be a guaranteed "solution."
My daughter is the exact same way. She's very leary of strangers or people she doesn't know well, and I see nothing wrong with that. She does
warm up to people after being around them for an hour or two, and I've thankfully never had anyone scold me for "spoiling" her to cause this behaviour. I was the exact same way as a child, and am still fairly shy until I warm up to a person (not quite to the extent that I was when I was young
). Besides, I'd rather her be leary of strangers, then have to deal with her running up to them wanting to be picked up. That could cause some problems. :P
My daughter goes to a sitter with another girl her age, a couple of times a week. The other little girl is the exact opposite of her. The first time I walked into the house, she ran up to me and said "up?" She'd never met me before. The sitter was telling me that it's a major problem for her, because when she takes the little girl and my daughter to the park, or for a walk, the other girl is constantly going to strangers, asking to be picked up. I shudder to think of what could happen if she ran up to the wrong person.
That's why I mentioned the daycare thing not being a solution. My daughter is around this other little girl for probably 10-15 hours out of the week, and has not picked up any of her extroverted habits. She's still my little shy girl. :P
Every kid has their own personality. You shouldn't be expected to train them out of it.
I also wanted to add that I doubt this behaviour stems from attachment parenting. Like I said, I was the exact same way as a child, and my parents were far from attached. :P I slept in my own room from birth, and was rarely held or hugged, as it was frowned on back then and thought to spoil children. I co-slept with my daughter until 12-13 months (at which point none of us were sleeping due to her wiggling, so she went to a crib and does quite well there). She's always been shy, whether sleeping in a crib or with us.
So don't let people scold you for "ruining" her by attachment parenting. That has nothing to do with it, imo. It's all about the child's personality.