I have known many immediate relatives of the U.S citizens and they have never had a problem. However, theoretically the problem exists. It would be right to do an immigration pre-clearance somewhere close to home.
Regarding your query on medical emergencies, you could tell them that your parents took the medical treatment. As long as there was no government funding I do not see any problem.
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Note: Unless the context shows otherwise, all answers here were provided by Rajiv and were compiled and reported by our editorial team from comments, blog and community calls on immigration.com. Where transcribed from audio/video, a verbatim transcript is provided. Therefore, it may not conform to the written grammatical or syntactical form.
Got my I-485 approval on March/26/2001, less than 2 yrs from when the labor certification application was sent in. I would highly recommend Rajiv Khanna to anyone looking for an immigration lawyer. Rajiv and his colleagues were all very efficient and prompt in preparing and filing the documents. Whenever I had any questions, they always replied promptly and explained everything clearly. Thanks a lot to all of them!