IMO, even if the part about the officer requesting it wasn’t there, the last part should also make it not apply in this situation. Catching criminals is a dangerous activity; that’s why the police are issued guns and clubs and tasers and kevlar vests. I have none of those things, so I consider myself to be at substantial risk of physical harm when trying to subdue some random guy.
I saw a cop chase LIVE on TV a few years ago, in the Southern California area, which was followed by a news camera helicopter and broadcast as it happened. The perp stumbled upon some outdoor event (it looked maybe a wedding, with people all around dressed up real fine). Three of those people took out after the perp, caught up with him, and took him down.
I wrote it up in more detail in this post, see Story #2 there.
Grab the purse; he’ll definitely let go.
Accidentally drop my crutches into the path and watch him trip if I am using crutches that day, otherwise give a gentle shove to my folded wheelchair into his path and put in an insurance claim for damage to the wheels. 
It would depend on my reflexes, but if they triggered, probably this. If they didn’t I’d just look dumb.
What’s a “Wife beater”?
One of those thin white undershirts without sleeves.
I’m the most popular guy at my Publix.
Years ago, I was checking out when some announcement came over the PA, like “Mr. Adams to aisle 3!” and I notice that all the male employees literally dropped what they were doing and took off running.
Quickly deducing this was a shoplifter call, I walked over to the doors and stood ready. Sure enough, this idiot rounded and aisle and headed for the exit with managers and baggers in hot pursuit. He was carrying - and dropping - baby formula all the while, and the guys just couldn’t seem to catch him.
I just stood in the doorway looking dumb (it’s easy) and as he got near, I took about 3 steps into him and put him down hard. My 300 lbs vs. his 140. You do the math.
After searching him for weapons, I dragged his ass to a cashier stand and stuffed him on the floor behind a register and had the manager sit on him until the fuzz showed up.
And twice I can think of off the top of my head, I’ve encountered a cop struggling to subdue and cuff a suspect and I jumped in to help.
I think if you’re an able-bodied guy - or gal - and you see an opportunity to help stop/catch some punk running from the cops, you should. It’s fun and rewarding!
And, the cops will remember you the next time you roll that red light!
Exactly.
ducati, that’s a great story. But around here, what you did would be a crime. (Several, probably)
In front of witnesses, and probably on camera. So I’m not going to be telling a story as cool as that. 
How is it a crime to be standing around minding your own business and have some shoplifter plow into you?
That wouldn’t necessarily be. This certainly could:
There’s a camera pointed at/around the register in virtually every store.
I would tackle him, partly out of civic duty, but mostly because I really, really enjoy tackling people.
IANAL, but that sounds like a legit citizen’s arrest to me.
I’d probably be reading and by the time I figured out what happened, it’d be all over.
Around where? If that were the case every loss prevention worker would be arrested and everyone could shoplift. Sounds like a legitimate citizens arrest.
We were always told we weren’t allowed to physically intervene with shoplifters. Take down a description of their car, pull the security tape and make a police report. You can tell them to stop but you can’t touch them. I almost got fired for chasing one guy out of the store because he always parked out of sight and I wanted to get a plate number.
Ontario, Canada mid 90’s.
That’s about how it’s handled in Colorado in 2011, last time I was working retail.
Any attempt to restrain anybody is problematic. "Legit citizen’s arrest’ isn’t as airtight as it might sound.
That’s got nothing to do with the scenario described in the OP, intervention by an outsider.
The cameras work for them and not against them, for one thing.
Missed the edit window, sorry.
I wanted to add:
The original scenario doesn’t even have a crime in it.
A guy with a purse is running, police yell “stop”. Maybe it’s his purse. Maybe he’s deaf.
We didn’t see him steal it and we don’t know why the police are stopping him- maybe there’s a bomb in the purse.
I believe ducati is a police officer, IIRC.