Disclaimer: I am a huge Duggar fan and think it's awesome how loving and close they all are and I have no issues with the number of children they have because they actually are able to take care of them, both financially and spiritually.
However, every time this topic comes up I can't help but wonder if Michelle truly practices "natural" nursing. By that I mean, does she nurse ASAP after birth, does she co-sleep, does she pacify at the breast, does she BW, does she bathe with her babies, does she cuddle naked with them? I had major struggles with ds1 and got AF back at 5 mos but had fewer issues with ds2 and didn't get it til 11mos. It took 3-4mos for me to "discover" AP with ds1 but was super-crunchy with ds2 from the get-go. If Michelle has BF issues to begin with, and then compounds them by doing any type of scheduled feedings (or hands her baby off to a "buddy" throughout the day), it's no wonder she bleeds again so soon.
And IMNSHO, scheduling (or in any other way interfering with) BF could be viewed as interfering with God's plan just as much as BC. So then I might go so far as to say that they wouldn't really be allowing as many babies as God wanted to give them; instead, they were artificially creating an environment where more babies would come than if truly natural BF practices were used.
It just really sounds to me like she has so many problems nursing that her period comes back sooner than it might otherwise. I bet if she had smoother sailing at the breast and was able to go to toddlerhood, she would only have a baby every 3 years.
I was tandem nursing number 2 and 3........I got my period back at 6-8 weeks, like with my other two births. Co-sleeping with them both. No pacifiers. Some of use get their fertility back real quick. She does mention she had troubles and I can see that might cause them to come back early, however those things you listed above does not apply to all.