How does one keep software proprietary while leveraging the GPL (aside from the case of not distributing it)?

There are a few avenues.

1. You incorporate GPL software and hope that no one notices and/or no one challenges. This is the most popular approach, and it’s quite successful, actually. 2. You cease to be a proprietary software company. Less popular, but an option.

Both of these are literally possible.

1 is a breach of license, 2 is not a solution to the problem, it is avoiding the problem.

Plenty of companies develop both proprietary software and contribute to GPL codebases. It’s not at all the dichotomy you think it is.

Just because it’s a breach of license doesn’t mean it doesn’t happen…

Plenty of companies also don’t allow their employees to contribute to GPL tools with company resources.