It’s a buncle. A carbuncle.
That must be Mazda’s CYA wording. When I said they were used for towing, I meant pulling them up onto a flatbed, which is what 90% of tow trucks are these days. That puts a lot of weight on the hooks so it’s odd that they say they’re only for tying the car down. But, the owner’s manual is aimed at the owners who might try to actually tow it across town using the hook which would be dumb enough to put in the manual “do not use it for towing!!”.
I think you nailed the Mazda question, but other manufacturers can be different. Infiniti G37/Q40 manuals call them recovery hooks and say to use them to pull the car out of mud/snow etc.
Some cars do have headlight washers that look similar. Audis come to mind because a lot of Audis have them, but some BMWs and other cars do too. Here’s a youtube video of one in action. It looks like a towhook cover. It’s hard to see in the video but if you look very closely, to the right and slightly lower is a perfectly round cover that is for the towhook.
Learned something new on the Dope today!
I have a 2010 Mazda3 and the wording in the manual has not changed on this item. I wish it were more specific - this link is suggesting the front eyelet is to be used for pulling the vehicle up onto a transport, as you say, but not for towing, proper:
*CAUTION:
Don’t use the tiedown hook under the rear for towing.
It is designed ONLY for tying down the vehicle when it’s being transported. Using it for towing will damage the bumper.
Tiedown Hook-Front…*
Perhaps the wording in the manual is what the lawyers say is all that should be said on the matter.
I have noticed some “designer” eyelets of varying colors on tuner cars - they are left there installed and exposed - I guess these guys are expecting to be towed a lot.
Because nothing says “expert drifter” like needing to have a tow-hook pre-installed to get you out of a ditch 
My Impreza and my father’s Forester both have these on only one side of the bumper. I will have to poke gently at it since it didn’t look like it opened.
http://www.mycarworx.com/artwork/CarWorx_Impreza_5Door_RearStepPlate_650w.jpg