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Being granted entry using the K-3 is VERY different than being granted parole using an AP. Entry is a much safer position than parole.
Would you mind elaborating on the portion of your statement above, as all my information conflicts with it.
As I've previously posted, in the context of an AOS petition, "continuous legal presence" in the US since the filing of the adjustment of status petition is one of the legal requirements for qualification. Congress provided a narrow exception to the physical presence requirement by directing that "an alien shall not be considered to have failed to maintain continuous physical presence in the United States for the purposes of sub paragraph (A) by virtue of brief, casual, and innocent absences from the United States." 8 U.S.C. 1255a(a)(3)(B ). The Attorney General, by regulation, interpreted an absence to be "brief, casual, and innocent" only if the alien obtained advance parole before leaving the United States or if the departure was out of the alien's control. 8 C.F.R. 245a.2(B )(6). "Advance parole" consists of the Attorney General's regulatory pre-authorization for an alien to be paroled into the United States upon arrival at the border without the appropriate visa or other documents necessary to enter lawfully. 8 C.F.R. 212.5(f).
The Board of Immigration Appeals has interpreted the statutory exception to the continuous physical presence requirement for "brief, casual, and innocent absences" as only preserving the alien's eligibility for legalization under the Immigration Reform and Control Act, and not as a substantive redefinition of an entry into the United States for other immigration purposes. In re Singh, 21 I. & N. Dec. 427, 434-435 & n.8 (1996) (en banc).
All that this appears to mean is that for the purposes of the "continuous presence requirement" found in AOS statutes, authorized brief, casual, and innocent absences are not deemed legal "departures" and/or "readmissions" to/from the US. For all other purposes, your rights, privileges and obligations under the law remain exactly the same as if you had to qualify for an "entry" under the applicable statutes. Likewise, as far as the ease of entry is concerned, it should not and, based on the analysis above, does not matter whether you are granted an "entry" into the US under K3 or whether you use AP to enter the US while you were previously here on a valid K3 visa. As such, for substantive legal purposes, being granted entry under a K-3 visa should be no different that entering the country via AP.
P.S.
Please do not misinterpret this post to mean that AOS applicants who have otherwise committed infractions of US immigration laws can leave and reenter the US with impunity if they just obtain advance parole (they can't). That issue is completely separate and distinct from the distinctions that are being discussed above.
The reason that's the case is because the courts have generally construed the "brief, casual and innocent" absences exception I discussed above as only applicable to the "continuous physical presence" requirement of legalization. It does not affect the generally applicable definition of what constitutes an "entry" into the United States under the law, since the courts have also inferred that Congress only intended to bestow travel privileges on lawful temporary residents (as opposed to the ones who were here unlawfully prior to their departure). This allows the border patrol to review the "entry" for compliance with all other legal requirements (other than the "continuous physical presence" requirement of AOS eligibility) which causes may cause significant problems for people who violated immigration laws prior to their departure.
, sadly enough, K-3s are NOT allowed to work until after that have their EAD [if Applied for at the same time as AOS] or have their Green Card in hand. K-3s cannot get their Social Security Number until they have at least the EAD in hand....Social Security guidelines 