A word similar in meaning to "platitude", but that does not imply truth

Solution 1:

Your title asks for a word that does not imply truth, but the body of the question seems to be asking for something that implies untruth. Words such as "platitude" and "aphorism" don't necessarily imply truth. If you want something that implies untruth, there's "hokum", although that doesn't have as much of an implication of being a cliche. You can combine "hokum" with other words to more strongly give that implication, such as "trite hokum", "cliched hokum", etc.

Solution 2:

A bromide or cliché is a familiar saying (which also works) that might or might not be true. Bromide connotes that it’s annoyingly moralistic, cliché that it’s overused, and saying is more neutral.

If it’s not a well-known saying, it might still be a banality, as well as trite, insipid and prosaic. These all connote that it’s uninspiring and boring, but not necessarily wrong.

Solution 3:

platitude is still OK. Lexico defines it as

A remark or statement, especially one with a moral content, that has been used too often to be interesting or thoughtful.
*‘he masks his disdain for her with platitudes about how she should believe in herself more’

This doesn't imply that the statement should be true; it could be either true or false, or it might not even be possible to judge its truth. What your definition is saying is that it doesn't matter whether it's true or not, it has become such a cliche that people don't really analyze its truthfulness.

And that's a good description of your examples.

In addition, you should realize that "do anything" is not intended to be taken literally, so it's unfair to say that it's false because you can't violate physical laws. But if you change it to something like "do anything that's possible" it's a tautology, since "possible" can be interpreted as what you can do. What's actually intended is "go beyond our current perceived limits". It's not meant as an observation, but as an aspiratioal or encouraging statement.