As mentioned in the comments, I think what you need to do is verify that you have obtained reliable data about the status of your battery before you come to any rash conclusions.
I am wondering why the tests came back fine unless there's a fault in my method?
Yes, there probably is.
Does this indicate that the battery needs replacing?
A trickle charger is one of the best ways that you can charge a car battery. It is much better (if you have the time) than the much more common and more convenient jump start. If a trickle charger doesn't charge your battery, likely nothing will. Also, do check the level of your battery acid because it could just be that it is low, hence your problem. Distilled water is good to use to top it up because the charge is neutral.
If you live in an area with a particularly cold climate, the quality of your battery is going to be much more important because a car in a cold environment will put a much larger strain on the battery than it would in a warmer environment. This could be a problem if you can't actually charge your battery fully (only to 50%) and you don't drive your car on a particularly regular basis (every two weeks).
If you think that you will be leaving the car stationery for long time intervals, or you live in a cold climate, also that you have verified the level of the battery acid and verified that you are testing the battery correctly, then I would definitely suggest that you replace your battery. Get a good quality one too (or wait until you can afford one).
If your climate if generally fairly hot, you plan to drive your car very regularly or due to further testing you have found that the battery status is actually fine (I suspect you might, as you said you had been to a couple of garages to get it checked) then I would suggest that you do not need to replace your battery.
One way to tell how healthy your battery is (and this is very easy to do), is just to start your engine and listen. If your engine springs in to life rather quickly - your battery is fine. If it sounds like it is trying to start for a few second and then eventually does, then your battery may need to be replaced.
Note that this sound will become more apparent if it is cold outside.
When I had my cam belt and water pump done at the VW dealership, they also did a standard check where they identified that my battery was in poor condition. After doing some more work on it myself with the interior lights and boot light on for the majority of the time, my battery became flat enough not to be able to start the car (this was on a really cold day). I just jump started it and so far my car has been fine, although I do still intend to get it replaced as you can hear the poor condition of my battery even in somewhat warmer weather to a lesser extent.