I think you´re right with your suggestion

This is a little more specific. The meaning of "verter" is to spill over into, and the wastewater is "spilling" into the public water system - it's not entirely clear that it's discharging into the water system on purpose or just spilling over.

For example, you have an oil "spill" - the oil isn't purposely discharged into the ocean.

The U.S. Environmental Protection Agency (EPA) Plans To Issue A ...
Plans To Issue A General Wastewater Discharge Permit To:. Alaskan Small Suction Dredge Miners ..... spillage into surface waters or to groundwater. ...
yosemite.epa.gov/.../bc30f88057c7455088256c870082cd07/$FILE/AKG375000%20FS.PDF

In this study suitability of an applied solid waste planning system for 22 villages and two ..... inherent and direct threat by way of spillage into the wa- ...
www.liebertonline.com/doi/abs/10.1089/ees.2006.0129


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Here's a good example:

spillage into the main waterline serving some 1.5. million residents of the Tel-Aviv, ..... systems when public health might be at risk was an ...
linkinghub.elsevier.com/retrieve/pii/S143846390470209

Engineer Felipe Ortiz Miranda has reported waste water spillage into Lake .... the potable water system from Lake Cocibolca to Juigalpa begun in March 2006. ...
www.envio.org.ni/articulo/3558



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spillage into the reservoir. .... e) A public agency must operate and maintain the sewerage system. ...
www.cdph.ca.gov/certlic/drinkingwater/Documents/DWdocuments...

mium, copper and zinc in the effluents from the company’s treatment plant. ..... Teberebe Goldfields Limited: 1996, Cyanide Spillage into Agonaben Stream, ...
www.springerlink.com/index/M716386656412246.pdf

The effluent line (pipe) that broke was the result of poor construction at the time .... More from all the sewage spillage into Islais Creek and the Bay. ...
www.islaiscreek.org/messages.html

I would use the whole term with regard to "autorización de vertido", and for waste waters "discharge" is preferred to "disposal", the latter more used for wastes or for wastewater land disposal.
And in the part regarding "vertidos de aguas residuales industriales a los sistemas públicos de saneamiento" I would say "industrial waste water discharge to public sewers"