Regular antennas are much less affected by trees, and such, but also not completely unaffected. More often, though, what gets in the way of regular antennas (besides the obvious: distance; and/or direct obstruction due to hillsides/mountainsides and/or buildings in the way, including the building the antenna is in/on) is mutipath. Multipath happens when there are objects, off the direct path from the transmitter to the antenna, for the signal to bounce off of (such as anything that would obstruct the signal, if they were actually in the way). Sometimes, that bounce actually helps, when it is the only way the signal reaches you. But generally, there are multiple objects for the signal to bounce off of, and in that case, you end up with multiple instances of the signal reaching your antenna slightly off from each other, interfering with each other. Without a link to the plot provided to you by tvfool.com, that's a reasonable guess for what's wrong in your case.
I use that antenna. It works great. However:
(1) All the television stations in Boston have their transmitters in the same place, up on the Needham flats. That's important, because the Terk HDTVa is directional; it works best pointed at the transmitter you're trying to receive signal from. There are other, omni-directional antennas, but they generally don't work as well as a similarly-priced directional antenna; in other words, there is a significant performance cost for providing omni-directionality.
(2) I am 13.5 miles, as the crow flies, from the antenna farm in Needham, and there are no hills or other topological obstructions - I have direct "line-of-sight". (On a very clear day, with very strong binoculars, theoretically I should be able to see the little needles of the antenna farm.)
If the transmitters in your city aren't grouped together, or are significantly further from your home, or if there are hills in between the transmitters and your home, you probably won't do as well as I do with an indoor antenna.
And indeed it is possible that your property can be fine for DirecTV and be unsuitable for Dish Network.