Would you feel deceived if a business's chat "agent"on their website, WhatsApp, or Instagram turned out to be AI and had hidden it?

I build AI customer-service agents for businesses here in the Gulf. They answer customers wherever they message website chat, WhatsApp, Instagram DMs take orders and bookings, connect to the company's actual systems, and pass to a human for anything sensitive. Here's my dilemma, and I want customer opinions, not developer opinions. Some of my clients don't want the agent to introduce itself as AI. I can live with that quiet greeting, good service, fair enough. But some push further: they want it to never reveal it, even if a customer asks directly "is this a bot?" they want it to dodge and route to a human instead of answering. As a customer, where's your line? The agent doesn't announce it's AI, but admits it honestly if you ask — acceptable? The agent actively avoids admitting it even when you ask directly — deceptive? Does it change anything if the service is genuinely fast and good? I'm deciding my company's policy on this and I'd rather hear how people actually feel than assume. TL;DR: clients want the AI agent's identity hidden across their chat channels, some even when customers ask directly. Would you feel lied to?