Does Global Entry require agreeing to a higher standard of behavior?

Looking at the reasons for ineligibility they list on their website, I think there are 2 items that may fit the case you describe. I would assume that you can become ineligible at any time, not just during the application process.

• Provide false or incomplete information on the application;
• Have been convicted of any criminal offense or have pending criminal charges or outstanding warrants (to include driving under the influence);
• Have been found in violation of any customs, immigration or agriculture regulations or laws in any country;
• Are the subject of an ongoing investigation by any federal, state or local law enforcement agency;
• Are inadmissible to the United States under immigration regulation, including applicants with approved waivers of inadmissibility or parole documentation; or
• Cannot satisfy CBP of your low-risk status.

I think lying to the customs officer (by checking this on the form) about not having fruit, but actually having it, would be considered a violation of customs laws. It could also be argues that CBP may think that the person's act of lying to the office / lying on the form, makes them look like not such a low-risk traveler. That last point can obviously be interpreted pretty broadly, which would fit the "higher standard of conduct" assumption.

As noted by phoog in a comment, another way to look at it would be that members of the Global Entry program are held to standards (in order to maintain their membership, not for other reasons) that general travelers are not held to. Global Entry membership should be seen as a privilege, and as such, it can be revoked pretty easily by the agency which administers the program (CBP).

Yes. When you go for your interview for Global Entry, you are explicitly told that you will be held to a higher standard and will be held responsible for "novice traveler mistakes," since in exchange for not having as much direct inspection to ensure that you follow the rules, you have to know how to and agree to follow them yourself.

Source: my Global Entry interview last year.

See the Global Entry Information Guide.

"If you violate any condition of Global Entry or any law or regulation of the U.S., officers may:" is followed by a list of possible penalties beginning with "Revoke your Global Entry privileges". The remaining penalties would also apply to a non-GE traveler.

It also calls out specifically "You must declare any fruits, vegetables, plants, insects, meats or meat products, dairy products, animals or animals/wildlife products, disease agents, cell cultures, snails, or soil."

I don't remember my Global Entry interview in detail, but I certainly got the impression that, by using Global Entry, I am taking personal responsibility for monitoring and checking my own conformance to customs and immigration rules, and in exchange CBP reduces the amount of their monitoring and checking. It is not a difference in the rules, but a higher standard of care. If I did not feel sufficiently familiar with the relevant rules to take that responsibility, I would not have applied for Global Entry.

Yes.

I've got Nexus, which is is Canada specific, but is a superset of Global Entry and I was given a warning when I didn't have the exact dollar amount of the goods that I was bringing into the country ready on hand with the receipts(I just knew they were below that duty free limit) and told that my Nexus would be revoked next time. The explanation was: Nexus(and Global Entry) is a TRUSTED traveler program, i.e. they TRUST you to know the rules and not slow down the express lanes. If you can't do that, you're welcome to go back to using the normal lanes.