50 bucks says that you have some bakers cysts forming.
Bakers cysts are essentially 'leaky caritilage issue'. When the cartilage gets torn, these cysts start forming in your knee. First your knee feels thick and pasty. Then it hurts to torque. Then you can't bend or can't straighten (or have to choose). EVENTUALLY they CAN get big enough to actually see. Sometimes they rupture which feels like someone poured acid down your calf.
Fix the cartilage, and it stops 'leaking' (oversimplification), and no more cysts.
The 'until proven otherwise' is actually a good sign. MRIs are great, but they don't see everything. 9x out of 10, if the MRI comes back clean, but the symptoms of torn CT are still there, and they go in? Yep, torn CT that just happened to be laying flat when you were getting scanned. What you doc did was to BELIEVE you. OTW, his other option was to say "It's clear. Go home." Instead, he's believing that your symptoms are real and that you're not drug seeking, and there's a real injury that the scanner didn't find.
The month out is actually fairly fast. I've had torn CT for months and years (different injuries), then gone in and gotten it fixed no problem. In fact, I'm strategizing with my orthopedic surgeon right now on the timing of some fairly minor surgery (essentially taking a dremel bit to my kneecaps to polish the cartilage that's gotten rough, and yep! You guessed it, I'm doing the baker's cysts things right now). 2 day recovery time, and then 2 weeks before able to run on it. It's a FAST healing surgery.
Sports med guys are used to doing this kind of strategizing / waiting for various surgeries, because athletes have seasons to get through... military folk waiting for leave... etc. It HURTS, but we're used to pain, so its more worth waiting for the timing to be right than to not be in pain.
On a fresh injury, with your MRI clear, it sounds like he wants to wait to see if it will self resolve. AKA if you don't really have a torn meniscus, but swelling pressing on a nerve. If the tear isn't showing up it is HIGHLY UNKLIKELY to be a 'severe' aka risky tear (where the whole thing can snap), which would be dealt with same week or on an emergency basis.
All that said? If you don't trust your surgeon, get a new one.
((To Cheryl's ETA... I've had my knees drained a few times over the years. Some are worse than childbirth... others are better than sex!!! OMG, the untold relief! It really depends on both the issue/area being drained and the skill of the person doing it. My worst ever was an ER doc who shoved the needle into my cartilage. Shudder. Just recently, it felt so good I could have married the doc on the spot. Did kiss him! I've only had 1 'blind' drain -where they just feel around- go well. The guided ones with xrays and contrast? Brilliant))