You were eligible..to apply. Spectrum or any ISP doesn’t determine your eligibility. Only Affordableconnectivity.gov (federal government website determines that)
Regardless, the reps make it seem like it's very easy to qualify if your kid gets free/reduced lunch. I assume that if you get handed over to a govt website an you click the "my kid gets free/reduced lunch" checkbox, that's all you have to do. This elides the detail that your kid gets free lunch because all CA schoolchildren do, which the ISP rep told you isn't a disqualifier. So at the very least, they're priming the pump for people to fill out forms incorrectly.