As Carmi said, it may have been older when you got it.
Also, the variety of watermelon matters. Some watermelons will keep for about three or four months, or more (unrefrigerated). These are sometimes known as winter watermelons. Varieties include such as Red-seeded Citron (not really like you'd expect a watermelon to be, per se), Navajo Winter, Santo Domingo Winter, King Winter and Wintermelon, among others.
Some watermelons need to be used as soon as they're ripe, practically.
The kinds you find in a regular grocery store are usually considered shipping melons (they have tough rinds). These normally keep longer than those with thin or fragile rinds.
Some possible reasons that a shipping melon would go bad fast include these:
- It may have been diseased.
- It may have been deficient in calcium, silica, potassium or other stuff.
- It may have been exposed to something before or after you got it (including fungus).
- It may have had perforations that were difficult to detect.
- If the fruit was unwashed, it may have had surface fungi on the rind that made it spoil faster. For at least one watermelon variety (Wintermelon), you're encouraged to wipe it down before storage. I don't know if that applies to all watermelons.
I've had watermelons I've bought from the store before (for 9 cents a pound—just thought I'd throw that in there) keep for several weeks unattended, under a table (in a college apartment). I'm guessing they were just fresh, healthy watermelons. It's not always easy to tell how long they'll last by looking at them, or feeling them.
If you can find the variety of the watermelon and where it was grown (Sangria might be a good guess), you might be able to find out more information about its susceptibilities.
Anyway, even though some melons can last a long time unrefrigerated, most of them probably last longer in the refrigerator, as Carmi said (although I wouldn't assume all of them would).