No, it's not. There is no abduction and no miraculous healing in the first place. Both assume the conclusion in how they are presented.
In every meaningful way the two examples are alike.
Absolutely not. There are indeed ways in which they are similar, and ways in which they are vastly different. You can find similarities in almost any comparison. However, you must qualify your statement that "in every meaningful way to you", the examples are the same.
Do you really not see the similarity between a claim of alien abduction or sighting made by a well respected member of the his community and a claim of miraculous healing made by a member of the medical establishment?
First there is anectotal evidence, possibly with a bit of confirmation bias in the people who reported the story. You'll note that you don't see a lot of white house press conferences on that alien ship people say they see so often.
While I'm on the topic I'd really like you to read what confirmation bias actually means. We see it on the forums here a lot. http://en.wikipedia.org/wiki/Confirmation_bias
This is it in a nutshell
Confirmation bias is an irrational tendency to search for, interpret or remember information in a way that confirms one's preconceptions or working hypotheses. It is a type of cognitive bias and a systematic error of inductive reasoning. These biases in information processing are distinguished from the behavioral confirmation effect (also called self-fulfilling prophecy), in which a person's expectations influence their own behavior.
Biases can occur in the collection, interpretation or recall of information. Some psychologists use "confirmation bias" for systematic biases in any of these three processes, while others restrict the term to selective collection of evidence, using "assimilation bias" for biased interpretation. In many reasoning situations, people avoid confirmation bias and test hypotheses in a genuinely informative way. The bias appears in particular for issues that are emotionally significant (such as personal health or relationships) and for established beliefs which shape the individual's expectations. Biased search, interpretation and/or storage have been invoked to explain belief perseverance (a well-established finding that beliefs remain when the evidence for them is taken away) and attitude polarization (when a disagreement becomes more polarized as the different parties are exposed to the same evidence).
Confirmation bias can lead to disastrous decisions, especially in organizational, military and political contexts. Attempts to teach critical thinking can be counter-productive if confirmation biases are not addressed, since by applying logical thinking only to one side of an argument, thinkers can become "actively closed-minded".
It is in large part the reason double blind studies are so important.
If someone were to tell a story of an angel coming down from the sky, and showing them a vision of heaven you might be inclined to believe it. You'd be even more inclined to believe it if the story confirmed some things that you already hold as true. Like whatever you think Angels are like and whatever you think heaven is like.
If you heard the same story, but the person said an angel came and took him to heaven, and stuck an anal probe in him and then killed all his livestock you'd be a whole lot less inclined to believe that.
Change it up only slightly and you have aliens taking a person to their space ship, and either showing them wonders of the universe in the spirit of 'Contact' or you have a story about anal probing. The livestock seem to lose no matter what.
Now, lets look at the medical doctor and this miraculous healing.
First, this sort of thing happens a lot. People heal all the time, and all over the world regardless of religion or location. That's why I said that if it was an amputation that was healed then that would be a true miracle. A woman regaining her sight is great, but we don't know what it was that caused her blindness in the first place. It could have been mega-pink eye or zombie bile or something. If her eyes were missing, or made of glass that's another story and on par with the amputation criteria.
(note: amputation criteria being an example of an unambiguious miracle that can't be explained by medical science.)
All that we know are claims.