I have seen these kind of statements with lots of various opinions.
To me, the answer to the questions whether a GC holder is allowed to return to COP is actually YES, you can, but do it at your own risk, since you are jeopardizing yourself of losing your GC.
It is true that once an asylee becomes a GC holder, his/her status becomes the same as other LPRs, with basically no restrictions. However, it is also true that one may lose his/her LPR status if he/she commits an act that makes him/her removable from the US under the law in section 237 of the Immigration and Nationality Act, basically if he/she violates any US law. Here comes the tricky part (or I would say the loophole), however, when when you return to the US/arrive from abroad, at the airport, you will usually be questioned by an IO officer before you are allowed to enter the US. At that point, if the IO established that by returning to COP you have actually make use of the system, meaning that you actually are not affraid of COP, meaning that you lied when you first applied for asylum, etc (which is a fraud or violation fo the LAW, btw), they, of course, can and will hold you for further investigation. Of course, at that point, you might be allowed to hire a lawyer and/or establish that your return to COP is legitimate, have a sound/solid ground. Nevertheless, it is your word against theirs, and at that point, you'll face trouble, regardless of the outcome. Trouble means, time and money.
Say may be like most people, including some ppl that I know personally, you're lucky and can enter the US without any problem, these questions could probably come up again when you applied for the CZ in the future. True, it may not come up too. How can you know? You can't and you don't.
Basically, IO can't accused those who got their LPRs status from other means that by returning to home country they have commited a fraud, unless they bring drugs or st, but they CAN suspect those who got their LPRs from asylum of commiting a fraud (that their asylum was fake it the first place, etc). Whether their suspision are well grounded or not is another problem, but at that point, what you will face is headache, no matter what.
IMO, this is the area of immigration law where you can interpret one way and the IO can and probably will interpret another way.
So, to me, yes you can go back home and come back here. Will you face trouble with immigration? Probably, cuz you, afterall are at the mercy of the IO. Will you lose your GC? Only if the court say so.
The bottom line is, if you go back to COP, you give the IO an opportunity to give you touble, as simple as that. Whether that trouble translate into losing your GC is another matter.
So, again, do it at your own risk.
