When you bottom-water a plant by putting it in a tray of water, it will saturate it from the bottom and work up to the top, even if the potting mix is dry. Some media, such as peat, will tend to repel water when totally dry, but I've found if it continues to be in contact with the water, it will eventually start soaking it up (it just takes a bit longer to get started).
The issue with watering only from the bottom is you eventually get built up salt, minerals, etc in the container; while watering from the top helps to leach them out before they get to levels detrimental to the plant. Personally, I like to bottom water when I let pots get too dry, which causes the peat-based soil to make a solid block, so water from the top just bounces off. But I usually just leave them in the water tray for a day or so to get it fully saturated and then remove. Otherwise I water from the top.
The biggest issue I've found from just leaving the pot in water is the potting media becomes waterlogged and turns anaerobic, which results in
root rot. This is especially true for containers made of plastic or other materials that don't allow oxygen exchange in the media.
I've also found it depends on the plant. My carnivorous collection is perfectly happy in a bog garden, where there isn't any drainage and the media is always saturated. My juvenile bald cypress
trees do great when I keep their containers in a tray of water during the growing season. Also, I tend to grow my trees I'm training for bonsai in plastic colanders to encourage root ramification, and they tend to do fine in trays of water (I assume because the colander allows enough air exchange to keep it from turning anaerobic).
So it really depends on many things, like media, container, plant type/growing preference, water source etc.