>At first, they explain the information is collected solely for medical reasons. Now they say they can use it as they please. Don't you see fallacy here?

Technically not a fallacy (as there's no logical fault in what they said). Just falling back on a promise to the public.

Not only that, it's also the counterexample to calling "slippery slope" a fallacy. After all, slippery slope is not a fallacy if the slope is, in fact, slippery.

It's not a logical fallacy, but it's still a fallacy.

You keep using this word "fallacy". I don't think it means what you think it means [1]

(a) a deceptive, misleading, or false notion, belief, etc.: That the world is flat was at one time a popular fallacy.

(b) a misleading or unsound argument.

(c) deceptive, misleading, or false nature; erroneousness.

(d) Logic. any of various types of erroneous reasoning that render arguments logically unsound.

[1] to paraphrase "The Princess Bride"

This usage fits definitions a, b, and c. This very definition draws a distinction between a 'fallacy' and a 'logical fallacy'

>This usage fits definitions a, b, and c.

No, it doesn't.

Government: - "We will use data just for medical purposes"

Government (later): - "Guess what, we lied/we recant: we will use them for other state purposes too".

There's nothing fallacious in (a), (b) or (c) way about either statement or the whole situation.