swear / military trailing

The following sentences are contents in a travel guide and I have no idea about the part unlined.
What is "swear" in this context?

And what is "military trailing"?

Would you take a look at them and comment some for me?

Thanks a lot~^^
pb

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ex 1)
The local population’s eccentricities alone are enough to leave a sociologist salivating: Evangelical Christians, patriotic militiamen, ranchers, new-age hippies, movie stars, ski-bums, pot-heads and even aliens (so swear the hard-core UFO recorders), all share the same high, alpine air.

ex 2)
Tourism is now a leading industry in all four states, with the military – there is a major presence in Colorado especially – trailing not far behind

thanks Vorpar,

As for the second question, I misunderstood it as the combination of the two words like "military trailing." Now it makes sense to me.

Still, as for the first one, "swear", it seems to me that the definition doesn't tell the meaning of the part...i mean the whole part including 'sword.'

Does that mean, 'there is truly aliens there... so... bring those hard-core UFO recorders'?

Thanks again for your consideration~!

thanks~!

your explanation makes sense to me.
Now I know the UFO recorders mean some people, not some device.^^