Normally the documents like AP and Re-entry permits are subject under the view of the officer at the POE, that is why they always said that your entry into the US is not guaranted, because even the USCIS is the one who issue it, is not a right nor a guaranty to enter. Actually is the same case as other visas like B1/B2,etc.
If you read the instructions in section III. Advance Parole Document starts with bold letters call "Travel Warning" which the burden is on the alien not in the USCIS and people ignore it or just don't read it. You are the one who must be accountable for your status and the use of your AP not USCIS. In part C of the same section explain just the two situations in where the AP shouldn't be issue. So in general, there is no situation that if you were out of status for more than 180 days or up to a year you shouldn't be issue an AP.
There are cases over the internet that I read and cover these cases: a) people who were out of status more than 180 days and got their AP and go out, came back no problem. b) same scenario but got stop at the POE and denied their entry. c) same scenario come back with no problem and by the time of the interview then get into trouble. There will be always the % of everything. But in my view the risks are too high. You can make an extensive internet search and find a lot of cases of all types.
Normally if you weren't out of status for the 3/10 year ban is very uncommon that you will have a problem at the POE just carry all your documents with you and a valid passport and of course don't get into trouble in the country where you going to stay or stay longer than you should be.
