All strawberries will rot and such if not taken care of. Sounds like you need a fungicide, and insecticide.
All strawberries are susceptible. Sounds like you need Captan for Botrytis Fruit Rot. Do not mix fungicide with basic water, it should be acidic. Use a mulch to keep berries out of the dirt. Pine straw works great!
Check the link for general info on strawberries.

Here is a link that might be useful: Strawberry info

I was describing the nature of the plant. I don't just stand by scratching my head. I thought I remembered as a kid seeing a neighbors strawberries being over 12" tall and holding up the fruit. So sagging to the ground is the norm?

Any specific recommendations on variety to get for eating quality?

Variety depends on location. What does well here, might not do well elsewhere.So I don't like to name cultivars. The site I linked describes good cultivars for different areas. I linked from the site I mentioned the page where they recommend plants by state. How tall a plant becomes can be a variety that is tall, and the berries are off the ground. My experience is some are off the ground, but some bigger berries never make it off the ground. So yes, it is normal for some to be on the ground. Nutrition is going to play a role. Also age of the plant. Something to remember too, is usually strawberries are good for 3 maybe 4 seasons Sometimes they last a year or two longer. After that the plant becomes weak and reduces production. It's best to always replace older plants with new runners every few years. Strawberry plants are very short-lived as far as productivity goes. See site on how to keep strawberry beds vigorous and productive. The older they get, the less they produce. At first production increases every year, but after 3 years production usually declines. If June bearing to keep plants healthy you must follow the renovation procedures. It is well described on the site I linked to.
For day neutral or ever bearing cultivars, renovation is not done. Only for June bearing cultivars.

If your bed is crowded, and not weeded, of course plants and berries are going to be small. Distance between plants is important. Strawberry beds have to be thinned constantly for productive growth. What you describe will happen to all cultivars with neglect.

Here is a link that might be useful: Stawberries by state

I received strawberry plants from (2) different sources both June Bearing but the varieties are unknown. Plants from one source are rather small and lack leaf luster and the berries stay relatively small and have a hint of sourness to them even when fully ripe. The plants from the other source are very healthy with vibrant green leaves and sturdy stems that hold the extra large berries off the ground and when ripe are quite sweet.

I continue to experiment with ground covering in the strawberry patch to reduce bug damage and to keep the berries clean from lying on the dirt and from dirt splatter when it rains. Straw works well but the runners have a difficult time finding the dirt to root and it does not break down quickly. When the berries are ripening, we are picking daily but we still lose some to critters.

We also do not use any chemicals in the garden as the kids enjoy taste testing directly from the plants. For the continuing health of the strawberry patch and garden, we fertilize with chicken poop pellets (not fresh as it is too hot and it will burn and possibly kill the plants).

I try not to use chemicals either, but if you get Botrytis Fruit Rot, you will always have it, and lose about 80% of the berries. It's wiped out complete farmer fields of berries.
Sounds like cckw has this, and putting in new plants will just be more food for the fungus.
Any berries you buy at the store are loaded with chemicals.
Sounds like both of you got old plants after they lost vigor. Runners from them should be fine.

Drew, I am reading the site you suggested (in bits and pieces as time allows, have pig flu in my house). If I want to renew my bed (raised with soil mix from sq ft garden book) Am I much better off regarding disease and fungus by switching to the next bed 3' away? I was originally just wanting to help the friend, but getting more interested in stepping up my own game. We get a lot of berries each year, but I know we could do much better.

Yes, good idea Sq Ft gardening is a fine method, and it would help, yes. I think the spores will be buried so deep they might not become an issue. But a new bed is even better. Grow melons, pole beans, radishes (super easy 30 days only for some) or tomatoes in the old bed. After a couple years you could go back to strawberries. It's always a good idea to rotate beds, and that is the better option. Start with new plants, as you might have a dud of a variety. Some places have 12 to 25 plants at fairly cheap, prices. I'll mention some internet sites if interested.

Drew I would like to hear your recommended vendors for strawberry plants

Indiana Berry for any berry plants. Good prices on raspberries. Not a super great selection but decent.
They sell strawberries in lots of 25 for about $18.50,
50 are only $23.50! These prices are actually high, but their raspberries are pretty cheap! I bet the plants are huge though. I bought raspberries and they were very big bare root plants.
Nourse Farms, even better prices. $12.50 at the most for 25 some are cheaper, and 50 are under $20.00.
Both these nurseries have excellent reputations.
Nourse probably the best reputation. Also nice is Sakuma Brothers. They sell in lot's of 10 plants for under $6.00

A few others are good too. But these are are really decent. Between the three many cultivars are offered.
Google the names and you should get the web addresses.