I just reviewed the GS ERS brochure - Platinum + online. It appears to be identical to the brochure I received with initial purchase a couple years ago and subsequent renewal of GS program.
If a valve stem is a tire service - and I presume it is - fixing that is not covered per se. Tire service is to mount a spare on a covered vehicle and possibly arrange for a mounted replacement tire to be delivered and installed. They will not buy you the tire or rim. You're on your your own for that and possibly more.
These "programs or policies" are very specific. If you don't like what they offer - don't buy them - and understand what you are buying upfront. The price of the GS ERS policies range from $79.95 - $159.95 a year depending on program. They routinely offer them at discounts or extend them and or upgrade them at a discount.
If you have a situation that is explicitly covered - your $6.67 - $13.34 a month premium is a bargain. But I don't see the premium a huge expense or ripoff just because some things aren't covered. That said - if you have a situation that isn't covered, there may be more affordable options.
My suggestion (and I have done this with them) is when they tell you what they will do and what it will cost - you have the right to ask for your ticket / order number and tell them you will call them back. Then see what you can arrange on your own - and or refer to your brochure to make sure you are getting the right deal from GS. If you aren't - call back and get it right. If you find a better deal - call back and tell them the deal you got and cancel your order. Or go with their offer.
Yes you have paid for service - but for a specific set of services - not every scenario under the sun. That would probably cost $7 to $15 a month