What does "having had" mean in this context?

I saw this paragraph in the book the autoimmune solution by Amy Myers, but I don’t know why it is using "having had the flu".

What's difference if this sentence was wrote as "Or you could be misdiagnosed as having the flu"?

At this point you might be saying, “Wait a minute! I’m sure that 95 percent of the people I know have not had mono.” However, you can be exposed to Epstei–Barr, develop mononucleosis, and simply never show any symptoms. Or you can be misdiagnosed as having had the flu. But 95 percent of the U.S. population does have the antibodies for Epstein–Barr, which means they were once somehow infected with it. And once you’ve caught the virus, it remains within your body for the rest of your life, whether you feel sick or not.

Andy Lin said:

I saw this paragraph in the book "The Autoimmune Solution" by Amy Myers. but I don’t know why it is using uses "having had the flu".

What's would be the difference if this sentence was wrote written as "Or you could be misdiagnosed as having the flu"?

At this point you might be saying, “Wait a minute! I’m sure that 95 percent of the people I know have not had mono.” However, you can be exposed to Epstein–Barr, develop mononucleosis, and simply never show any symptoms. Or you can be misdiagnosed as having had the flu. But 95 percent of the U.S. population does have the antibodies for Epstein–Barr, which means they were once somehow infected with it. And once you’ve caught the virus, it remains within your body for the rest of your life, whether you feel sick or not.

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The difference is that the original suggests that the misdiagnosis might be that you previously had flu, not that you have it at the time of diagnosis.

"as having the flu" [ now]
"as having had the flu" [ in the past]

teechar said:

"as having the flu" [ now]
"as having had the flu" [ in the past]

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Can I say "Or you could be misdiagnosed as having the flu" to present past tense?

Not past tense, but past time:

He was diagnosed last week as having the flu.

Andy Lin said:

Or you can be misdiagnosed as having had the flu.

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That "can" is about possibility, not ability.
Therefore, even if you change it to "could", or even "may" or "might", the sentence would still be about possibility.
Does that answer your question?