About how old do you think the tiles are?

The house was built in 1963 and they are 12"

The tile has to be tested by a lab. Look in the yellow pages under Asbestos Abatement / Testing. You will normally get results back in 48 hours.

I'd get all the loose tiles out of the house for now and then cover the floor with a tarp to keep any dust down until you find out. It's only dangerous when it gets airborne by sanding, sawing, ect.

There may be asbestos fibers in the black adhesive also. So...don't sand, scrape or crush any of the tile or the adhesive. The fibers in both the tile and the adhesive are locked in place and only become airborne, as Jerry said, by sanding, sawing and doing anything else to pulverize the material.

If they came up real easy as you say, then you probably have little to worry about. Have the tile and adhesive tested and then decide what your next step will be.

The advice you received is correct: The best way to deal with old asbestos floor tiles is to cover them up. That's enough to prevent the damage and wear that can release fibers into the air; no sealer is needed. Carpeting and a suitable pad will do the trick.
To determine whether the acoustic texture (or floor tile, or siding, etc.) contains asbestos, place a small sample (about the size of a nickel) in a plastic zip lock bag and mail to an NVLAP certified laboratory. The cost for such testing in nominal (about $20), but three separate samples are generally recommended. Ciciliot