The Example is poor
A Modern car is complicated but highly reliable for the same reason that Lego can make complicated structures but still hold together reliably.
They are both restricted to 4D interactions.
There are of course a few more principles at play such as:
- Well defined interfaces
- Mass Produced
- Quality Assurance of components
Compare that to software code. The 3rd, 400th, and possibly all lines between 2001- 69876 can influence variable
A which then influences...
The dimensionality boggles the mind.
Now if you write code and restrict yourself to the low tens of dimensions, and implement other principles like: well defined interfaces, mass production, and quality assurance you can indeed approach levels of reliability found in cars.
In fact these systems exist, such as the flight avionics in planes. These are modular with well defined interfaces, each module is itself redundant with each duplicate produced independently by competing teams, and quality assurance is thrown at every component and assembly.
Your boss is correct in assuming that a larger code base is riskier, because that extra line can push the dimensionality of software higher. Higher dimensionality makes a larger result space that must be quality assured.
As there is only so much time in the world, only so much of that result space can be verified. The greater that difference the riskier that code base is, because it is less likely day to day operations will stay in the verified region.
You are correct in that applying good engineering practices allows you to reduce the internal dimensionality and as a result the size of the result space. It also allows you to verify regions of the result space much more reliably and in a more timely fashion.
I think you can also agree that the most reliable code, is the code that does not exist.