Anyone who has worked with the big vendors knows that the correlation between quality and price is very loose. The lowest cost provider is rarely great, but the high cost provider can also be selling you a lot of juniors.
Probably why parent mentioned finding a smaller company. I don't know about the Indian outsourcing market specifically, but in many sectors it seems a few mid-sized companies are the best for this sort of thing.
Which also means you need to find the right one for your problem, your purchasing department won't be set up with them, and you won't be able to just order as much capacity as you want, so getting there is hard.
But that probably works in most cases/places anyway.
But then the price mysteriously increases to the point where you might as well have hired them on-shore and you're not saving any money.
So, do you want to save money by offshoring everything, or do you want to get good people to actually do the real work that needs to be done?
They got where they are by doing what they are doing. Spending years on your project is something else.
I don't need to drag the building architects, master masons or master carpenters to help frame every wall of the house; ditto for code.