To be honest, I'm really disapointed from Maple.
I mean, when I use an algebraic computing system, I expect it to deliver correct and reliable results.
The documentation of testeq says:
"The result FALSE is always correct; the result TRUE may be incorrect with very low probability."
And now - as you said - it comes out, that FALSE can really mean "false" (= equations are not equal) or it can mean "don't know". It should - at the very least (!) - state "don't know", "too lazy", or whatever, when it cannot give a correct answer.
As it is now, the result from testeq is worthless: FAIL is unreliable, TRUE may be incorrect with a low probability.
That this is documented in the help system does not really help. Do I have painstakingly dissect the help system of any command I use, to find out, if and in which special circumstances the command is usable? The descriptions of the commands are often several pages long and not easy to grasp. I would expect, that Maple says it clearly by itself, when it reaches its limits.
In this example testeq is a simple function and my equations are quite simple too. That Maple fails in so simple circumstances makes me very suspicious. I don't know if I really shall relay on it for important calculations. In other words: shall I use Maple any more?