The agent is absolutely correct. The official policy is that if there is a legal connection leaving on the same calendar day that results in a layover less than 8 hours, you would not be eligible for the STPC benefit.

Let's look at the alternative (as an example). There are a number of routes that have one daily service only (eg. Accra). I regularly fly the route from Mumbai to Accra. There are 5 daily flights leaving Mumbai pretty much evenly spaced around the clock. The 4am departure from Mumbai connects immediately to the Accra flight. However, if I decided that I "don't really want to" fly out at 4am and instead fly out at 9am, then I would have a 21 hour layover in Dubai before the next departure to Accra. Is it really logical that Emirates should provide essentially a complimentary vacation with free hotels, meals, visa and ground transportation just because I "don't really want to" take the connection that they already do provide?

That said, Emirates' agreements with the STPC hotels are for block bookings. That means that a minimum number of rooms are paid for at a flat rate regardless of whether they are used. If there are already paid for rooms going empty, then the STPC desk staff will often authorise "exceptions" for passengers that are otherwise ineligible.

The nationality of the passenger sometimes determines their eligibility for these exceptions. A cousin on an Indian passport traveling on the same PNR with with an American friend was denied the STPC (flying BOM-DXB-GLA on an otherwise ineligible itinerary) while the American was given the voucher. The reason cited was that UAE immigration might not approve the transit visa for an "unmarried woman" from India traveling without a male chaperone. In the end they just shared a room at the airside transit hotel at their own expense.