I believe that it all depends on the industry and on the type of product/service offered to the customers. Also, what are their general expectations?
For example, iPhone is a US product and might be advertised as such. Even though, the displays are made in Japan and South Africa, sensors are from Taiwan, as well as other components made in Germany, France, Italy and the Netherlands. All these raw materials are then assembled in China. Despite all these, for the customers, the iPhone is an American product and it can also be advertised as such. For the customers, the little details of the making of the iPhone do not really matter. Furthermore, Apple do not try to actively market the iPhone as a product made in the US with raw materials exclusively outsourced in the US either.
On the other hand, few years ago in France, restaurants were advertising the food they sell as “homemade cooked”. People were being largely deceived as what was being served to them, was frozen food made from factories.
The restaurants owners used a loophole to achieve this deception legally. The law now has changed, and you can only call “homemade” the food that is being cooked from scratch from raw ingredients.
Here we can see that, although the owners did something which was legally right, yet people felt deceived by what they did.
So for me from a shariah perspective, we need to assess each case individually. However, if you can have a disclaimer or mention somewhere, that services might be outsourced to others, then there will be no issue what so ever.