There's no evidence in this article or the cited articles that Uber/Lyft are seeking to subvert public transportation or are working with the Koch organization. It says they are partnering with public agencies to supplement mass transit. This might be part of a bigger scheme, but there's no evidence presented that they are lobby against public transit at all.

IT has baffled me why government continues to stand in the way of private mass transit. Sydney opened its system up to private lines and it has flourished, whereas the DC Metro system is just one more wreck from total collapse.

Hugely undesirable.

Competition is good for the consumer. And public transport is a competitor in a way

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The company continues to heavily subsidize per-ride costs to inflate its value to investors and undercut existing options, despite bleeding billions of dollars. “Uber is effectively a middleman for a money transfer from venture-capital (VC) firms to consumers,” writes James P. Sutton in National Review. Simply put, effectively supplanting the taxi industry wasn’t enough: Uber plans on undercutting public transit to finally turn a profit.

If Uber can undercut public transit, I'll be impressed. Fares tend to cover 30-40% of operational costs of public transit, and if you include capital costs, it will be even less. With the amounts of subsidies public transit gets from the taxpayer, even the venture capitalists can hardly compete.