Why use an antistatic solvent dispenser bottle?
Generally speaking ESD protection is a bigger concern in larger scale manufacturing and production setting than it is for the homebrewer or r&amp;d engineer. 

The can specifically can pick electrostatic charge from you as you are moving around the house/shop and can store that charge as a weak capacitor at high potential. Your concerns about 12" is a general recommendation about keeping potential ESD sources away from sensitive electronics. 

It is also quite likely that the manufacturer of the "non-ESD safe" version of the product container simply never bothered to go through ESD-safety verification or simply wishes to create a more expensive product for customers that require that validation.

If you are working at home or in a small lab it is very likely that you will have no problems using either product and ESD may not even register as a concern.  At the very least you could test the product in house quickly and be confident that its ok to you. On the other side of the coing in a manufacturing setting a technician may be running around to multiple stations and working with a much higher volume of devices that purchasing verified ESD safe products becomes a valid business concern. 

To specifically answer your question, if ESD is a concern to you, you will be safer as a general rule keeping non-esd rated items 12" away from the device or have a system to bleed charge. Keeping a solvent can on a grounded ESD pad will probably be enough verification for me personally . After all, a person is the biggest ESD danger in the room and you are comfortable handling the device after ESD precautions are taken.