How it works in reality will vary from place to place, and I only know what I was told in school. I was never a first-hand witness to this, like I said earlier, so you'll want a better source for exact details.
The way probation is supposed to work is the way you said: PD and probation/parole are separate entities and aren't supposed to be colluding. But the two entities do collude, in order to skirt the law. The degree of cooperation/abuse will vary, if it happens, so my purpose was just to shed some light on this, so that people know what's going on. This stuff isn't just a matter of keeping your nose clean when on probation. If a probationer lives with you or has lived with you recently, or carpools with you, or shares a storage space, or even just spends time at your house (that one gets sketchy), etc., you can be searched. We should all know about it.
Trivial example: PD is looking for a guy who robbed a 7/11 wearing a particular hat, using a particular kind of knife to intimidate the clerk. They suspect you, or a roommate, or someone who uses your car (etc.) but they lack probable cause to search you and don't have a warrant. Your probation officer knows nothing about this, and has searched and drug-tested you just a day or two prior. Maybe he/she noticed the hat, which is legal to own, and the knife, which is legal to own, but thought nothing of it, since PD and p/p are separate entities. Let's assume you're innocent, and live in your parents' spare room after getting out of prison for retail theft, or something similar.
Local PD calls your probation/parole officer, asking for a quick favor. Someone just robbed the 7/11, and they want that 'random' search that usually comes once a month (or however often) done immediately. Now, in effect, you're being searched for the hat and the knife, without any probable cause, and without a warrant. Your room is searched, as usual, but this time they shake the entire house. Your parents' room, their cars, common areas, your kid sister's room, etc., are all trashed. Unlike previous searches, your family's computers and cell phones are taken for review, along with any other storage devices.
You're not guilty of the robbery, but your similar-looking hat is taken as evidence, as is your dad's similar-looking pocket knife. PD is convinced you're the guilty party, and is applying all possible pressure. Your probation officer was a reasonable person, and had really wanted you to succeed. He/she had been searching only your actual room and common rooms, but, doing PD a favor, your offense has now harmed your entire family, who have had their privacy violated, property confiscated, and may be harmed financially.
Your family, or roommates, aren't going to tolerate it a second time, so you're evicted. You risk violation of your probation/parole by not having a residence. You check into a motel, but the next day you're searched and drug-tested again, this time in the middle of your shift at work. Your coworkers watch you being escorted away by police and your probation officer, who again requests police presence for his/her safety. You're fired the same day. The money dries up and you can't afford your motel room. You're in violation of your probation or parole. Police have forgotten about the 7/11 by then, but probation/parole violation is treated as a new, separate offense. You go back to prison.
That all might sound far-fetched, but I just strung together a few of the abuses that I have heard about, which all can and do happen, legally. I'm hopeful that this is all rare, but anyone who has any contact with an ex-convict should know what can happen.