In the U.S. system, no visa (including a green card==permanent residency) constitutes permission to enter the country. A visa only enables the holder to travel to a port of entry and request permission to enter the country. That permission may be granted or denied regardless of the specific visa category. Even if you have a gold-plated, von-Neumann-league visa... if the employee at the bottom of the CIS/CBP/* org chart who takes your passport is having a bad day, you'll be on the next outbound flight.
Only U.S. citizenship implies a right to enter the country.
No, LPRs are sort of an intermediate category. CBP can't take away your LPR status, only an immigration judge or court can. So CBP has to let you in although you may be given a notice to appear in an immigration court. Trump discovered this when his administration tried to bar green card holders from muslim majority countries from re-entering the US.
That's a dangerous oversimplification. Say you are a US lawful permanent resident. CBP has the power to deem your LPR status as having been abandoned (e.g., if you've been spending too much of your time outside the US, or established sufficient ties==primary residence in another country) or revoked (e.g., if you've committed one of a variety of crimes, which include any conceivable threat to national security). That determination depends only on the CBP officer having reason to believe that's the case; there's no need for any judge to get involved. Incidentally, many [0] believe that refusing to give CBP full access to the data stored on your personal computing device(s) can constitute sufficient grounds.
Once that happens, CBP can initiate expedited removal proceedings: you are forced into some cell in the airport, without access to legal counsel or any possibility of communicating with the outside world, in some cases without access to the medications you need to take... until it's time for the next flight to the country that issued your passport. Since you've effectively been deported, you can get hit with a 5-yr ban on reentering the US. And you'll have a lot of explaining to do every time you apply for a visa for any country for the rest of your life, because the "Have you ever been deported?" little question is everywhere.
All this could happen, and has happened. (Not going into the side issues of what it takes for visas in various categories to be revoked, or why Trump's travel ban got watered down: which actually happened for a different reason)
Do you have an references for expedited removal being applied to LPRs? That link you included has this:
"Lawful Permanent Residents (green card holders or LPRs): You only have to answer questions establishing your identity and permanent residency (in addition to customs-related questions). Refusal to answer other questions will likely cause delay, but officials may not deny you entry into the U.S. for failure to answer other questions. LPR status may be revoked only by an immigration judge. Do not give up your green card voluntarily!"
Which strongly implies that CBP can't use expedited removal or consider you inadmissable when you apply for entry. You could certainly be detained until you are seen by a judge though (probably not much better) and I've heard of people being pressured by CBP to fill out a I407 (surrendering your LPR status) and then being removed.
Only U.S. citizenship implies a right to enter the country.
EDIT fix typo