The Mercedes F1 team appears to be one team that makes cars with engines that they also supply to other teams. However it is not quite like that. The engines part of the business has been going for a long time with McLaren since the mid 90's and before that they were 'Ilmor'.
Then, five years or so, Mercedes bought what was the Honda/Braun constructor team. Both the engine business and the car constructor part of the empire are in the UK albeit geographically separate.
It would be unsporting for Mercedes to supply their on-track rivals with lesser engines, particularly since they pay top money for them. So the official PR story for this is that the separate constructor part of the business came up with this innovation all on their own for packaging reasons, i.e. a more aerodynamic car.
There is no foul play going on, Mercedes planned this from the start. They knew that coming back into the sport they had no chance to catch the dominant Red Bull cars so for the last 5 years the team has been solely focused on developing a car for this season's rule changes. Mercedes intentionally made the decision to have a worse team the last few years to put more money toward R&D for this season. This sacrifice culminated in them having a better designed car than any other team this year with their innovative turbo/compressor placement:
Your engine point is moot, because it is up to the team to implement the supplied engine and there are huge monetary differences between teams. A team buying supplied engines is always at a disadvantage in terms of time and design because they didn't design the engines. They have to adapt their car to the engine, while the manufacturer team can develop both in concert. Its similar to Android vs. the iPhone, Apple's products use similar parts but the experience was better because its OS and hardware were developed together, instead of hooked together at the end like Android phones. Also, F1 is not fair in terms of money. Manufacturing teams, Ferrari, McLaren, Mercedes etc, have R&D budgets multiple times the size of the smaller teams. Even though, Force India buys Merc engines, they have a fraction of the budget to figure out how to optimize it, and terrible drivers in comparison.
The interesting bit about the Ilmor relationship is that it stemmed from development of another Mercedes' branded motorsport superweapon.
Ilmor was founded by 2 Cosworth engineers who disagreed with the development direction of the DFX CART engine, they started with funding from GM to design an Chevy-branded engine for CART which went on to win 6 straight Indy 500s. Despite their immense success, the Ilmor team wanted to design a one-off engine around a loophole that allowed much more regulatory freedom if the engine used pushrods instead of overhead cams. That loophole could theoretically allow an engine to make ~200hp more than the competition butGM was winning trophies hand over fist. They declined to fund the concept so the two companies parted ways.
They still saw enormous potential in the pushrod concept and found willing partners in Roger Penske and Mercedes. Shortly thereafter the Mercedes 500l had been born, also known as Mercedosaurus Rex. It's the spiritual predecessor to this year's engine in that it was in a completely different league than its competition.
Then, five years or so, Mercedes bought what was the Honda/Braun constructor team. Both the engine business and the car constructor part of the empire are in the UK albeit geographically separate.
It would be unsporting for Mercedes to supply their on-track rivals with lesser engines, particularly since they pay top money for them. So the official PR story for this is that the separate constructor part of the business came up with this innovation all on their own for packaging reasons, i.e. a more aerodynamic car.