From pjiang: 1/19/09, even LPRs have to give biometrics when ret

Here is the Final Rules from US DHS (from website):
Effective January 18, 2009, the following additional non-U.S. citizens will be required to provide biometrics when entering or re-entering the United States:

* Lawful permanent residents of the United States (LPRs);
* Persons entering the United States who seek admission on immigrant visas;
* Persons entering the United States who seek admission as refugees and asylees;
* Canadian citizens who are currently required to obtain a Form I-94 (Arrival-Departure Record) upon entry or who require a waiver of inadmissibility to enter the United States (this excludes most Canadian citizens entering the United States for purposes of shopping, visiting friends and family, vacation or short business trips);
* Persons paroled into the United States; and
* Persons applying for admission under the Guam VWP.

Now, my question is what if the LPRs have prior arrests or minor offenses which had been inspected and adjusted by USCIS and granted LPR status---will CBP refuse the entry of these LPR to US?