A friend shared this article and I'm curious on others thoughts.

Not sure what the purpose is of the article.
The picture put up is not lateral flexion, it is a lateral bend or "tipping the nose ,they are two different things. Bending a horse, as pictured, has very little benefit to me, since  his poll is not even with his nose perpendicularly. 
Disengaging the hind end requires a leg yield to disengage the hind end while tipping the nose. 
Yes, true lateral flexion will engage the hind end while softening the ribs. 

If you're going to pick on someone, at least be able to articulate and make sense. 

Am I wrong on bringing her around like this to stretch her neck/poll?  I'm doing it on the ground and using treats to bring her around in both directions and down between her front feet.

Your're not wrong to do stretches, but the horse in the picture is not doing stretches. 

Coming from a reined cow horse and cutting background. I despise trying to get a colt to work a cow properly if someone else started them using those exercises-  asked for the nose without the feet moving and overdoing the disengaging the hind quarters. Of course I need to move the hips but I've ridden horses behind others that overdid or taught it incorrectly. Everytime I wanted the nose tipped to the cow, use my inside leg to move the ribs out of the way they want flip their hip out disengaging when I want the hip engaged.

I also want the rein to be connected to foot. It seems the ones taught to give the nose ay a standstill tend to run out through the shoulders or dump the outside shoulder bad.

I feel like the originator of the post you're referring to took the training technique totally out of content.  If you have followed some of these clinicians one would know the reference to lateral flexing while standing is just the first step in their program.  They follow up one rein stops which can be helpful  in case of emergencies, disengaging hindquarters, vertical flexion etc.... 

One certain clinician "CA" did a training series with a profession barrel racer all the above was shown and demonstrated, very helpful to see the techniques applied to barrel racing. 

As with any tool......its good to have them....and use what works for the job....imo

I learned that giving the nose easily to either direction at a standstill was the first step to a nice headset. 

I've been training n picking  n raising my own horses since I was 7  62yrs. I train them for several events and never done a lateral flexion on any of my horses. My horses are all around n tops in every event. NFR horses. I never take my horses on opposite sides of the barrels or opposite direction to keep the horse guessing which way to go. When u run large arenas especially pacific NW you do not want these horses confused not even in small arenas. . In all the yrs of running I've never had a horse run off pattern. 

It's about having the head neck ribcage n the horses entire body balanced . Also depending on the horses. The horses I ride n train have quite a bit of TB not the distance TBs the sprinters that look like Qtr horses they are easy to train learn fast that are very soft, it's bred into them. I think the flex techniques works for alot of the Reiner's possibly.