Wow, usually they will make the call after 1 hour! That's scary they were so impatient. I have to agree that lack of nipple stimulation would/could have contributed, and tugging on the cord is never a good idea, and yes, if you delay the cord clamping, a lot more blood can drain out of the placenta, making it easier to come out.

Something to keep in mind next time is even if bub isn't actively nursing, you can always stimulate your own nipples, or get your partner to do it...

I'm very glad to hear you would go elsewhere next time!