That is correct, the local or major airport can restrict flight, or impose an altitude limit with in their airspace.
You can contact Yuneec once you get your part 107, they will supply firmware to unlock the NFZ restriction.
You will still be required to report to a local airport if you are going to fly with in in their airspace.
The first part is somewhat incomplete. It's true if you're inside the airspace - but note that not all airspace extends to the surface, or for 5 miles from the field. Class B and C airspace looks like an inverted wedding cake, and the further from the field, the higher the airspace floor. If inside the 5-mile range, but you're outside the airspace, it is not true. The to-the-surface airspace doesn't always reach 3.7mi from the field... I didn't see the OP give an exact location, or otherwise indicate that he's inside the airspace, just how far he was from it.
OP, you might want to get the VFR Sectional chart for your area and determine the airspace where you are...
See para 7 in the "Flying for Fun Under the Special Rule for Model Aircraft" section of the FAQ, at
Unmanned Aircraft Systems (UAS) Frequently Asked Questions. It says:
"
Can an airport operator object to model aircraft flights near an airport?
Yes, an airport operator can object to the proposed use of a model aircraft within five miles of an airport if the proposed activity would endanger the safety of the airspace. However, the airport operator cannot prohibit or prevent the model aircraft operator from operating within five miles of the airport. Unsafe flying in spite of the objection of an airport operator may be evidence that the operator was endangering the safety of the National Airspace System. Additionally, the UAS operator must comply with any applicable airspace requirements."
Bottom line: yes, you have to advise. Yes, they can say they don't want you to. NO, they can NOT tell you that you cannot. Yes, if you fly anyway, and cause a problem, you're super-screwed, not just screwed. If you are actually inside their airspace (and it's to the surface at your location), THEN they can tell you no and it sticks [basic meaning of last sentence in FAQ para in context of this thread].
Example... I live under the pattern (and therefore inside the surface-2500 class C airspace) of a military airfield. I also volunteer at a local rescue squad, which has 2 nearby stations (one inside the 25/sfc airspace, the other beyond the airspace, though within 5 miles of the field). I call the tower to ASK to fly in my backyard. I've been told no only when the overlaying restricted area is active (it happens, but is rare and usually brief), and they always otherwise approve, as I do not exceed ~125' AGL (the height of some nearby trees) and they know my cell number and that I will land immediately if it rings. I also ASK to fly at the closer station, with the same results. At the farther station, I do not ask; I advise, and verify that the restricted area is not active.
There's a positive side-effect that most people don't realize about ATC clearance inside airspace. I was ... accosted by a local Sheriff Deputy recently while prepping to fly at the closer station - he misunderstood the rules and thought < 5 miles is no fly, period. I told the Dep that we are inside the base' airspace and I have their permission. I called the tower back and he found that if he hassled me further, THEY would file charges against him for usurping their authority over their airspace. Helps to work with controllers (I'm an ATC Systems Engineer). Civilian airfields may be iffy about enforcing their jurisdiction over other authorities regarding their airspace, but a military field is almost certain to do so. Knowing this now, I fly inside military airspace - with approval - whenever possible.