Whatever they’re paid it’s not a salary. They receive a compensation for the lack of income while holding office.
They are federal employees. The fact that they got their job via election doesn’t make them not federal employees. It does make them not members of the civil service, though.
What in the world does that even mean? What do you think a “salary” is?
Unless there’s a citation that contradicts me, I’m going to say that this is wrong. The president, members of Congress, Supreme Court justices, etc., are not employees of the federal government. Collectively, they constitute the constitutional government. Is AT&T Inc. an employee of AT&T Inc.?
It means being a politician is not an occupation, whatever politicians believe. While you hold office you act as an agent for your voters and don’t have time to earn an income in an honest way. 
Thus you get compensated by the state, community or whatever.
“The government” as a corporate entity is separate from the people who run it. That’s why people charged with federal crimes are charged by The United States and not the president. We left that sort of thing behind when we got rid of the king.
The proper analogy is in comparing the CEO of AT&T to the president. And the CEO is most definitely an employee. (One might also consider the board of directors of a company, most of whom aren’t actually employees, and that’s why this is a bad analogy.)
I decided to do some digging. There’s some interesting variations in the statutes for this sort of thing.
On the president:
On the VP:
On Congress:
On the Supreme Court:
So my conclusion is that there’s no particular standard about what the compensation of senior government figures is called, and your quibble about “salary” is a nonsensical semantic argument.
FWIW, my guess is that the only reason the president’s salary is referred to as a “compensation” whereas the VP’s is as a “salary” is because that’s how it’s worded in the constitution.
BTW, did you know that Congress Critters get their pensions from the Federal Employees Retirement System?
The president doesn’t even have to do that. I’m too lazy to cite the exact text, but it actually just says the president will communicate from time to time about the state of the union. He doesn’t have to give a speech – he could just send a written report. In fact, many of the early presidents didn’t give a SotU Address. Giving a speech became standard some time in the middle of the 19th century, but I forget which president started the practice.
The equivalent of a reprimand by Congress would be a resolution (either House, Senate or Joint) about whatever issue they didn’t like. The resolution would not be binding law, just an expression of Congressional displeasure. I suppose that the Senate could fail to convict and issue a resolution instead.
That would be a concurrent resolution, not a joint resolution.
Completely unaddressed thus far is the likelyhood that random drug testing conducted by the federal government is unconstitutional.
Yes, they engage in it, but this is not proof that it is, in fact, a permitted activity, just that it has not been successfully challenged.
Random drug testing, as opposed to drug testing conducted with cause (say, in the wake of an accident or testimony of drug use), seems to be covered here:
“the right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.” (4th amendment)
Obviously the framers of the Constitution could have not predicted the use of urinalysis or other forms of testing for drug use, but they still managed to cover it, imho.
Of course, it can be argued (as has been) that random drug testing as a condition of employment IS “reasonable”, but it is certainly the case that it is a search and seizure conducted without a warrant and without “particularly describing” the “things to be seized” (only a very general description of traces of illegal drugs, not, say, “we have reason to believe this individual has used cocaine and we expect to find it in his piss”).
At any rate, the President is probably poked, prodded and tested more than the average citizen in the course of medical exams and any such drug use would turn up. But given the confidentiality between doctor and patient, I doubt his records are turned over without his consent for inspection. And I can’t imagine he would be subjected to random drug tests.
President Obama did recently say (on The View) that he doesn’t Twitter or engage in other social networking on his phone because all his accounts, including email, are monitored, so he lacks the privacy of the average citizen. But I’ll wager he enjoys more privacy when it comes to the contents of his urine than the average joe with a job, sensitive in nature or otherwise.