Knee injury and xray shows no broken bone. No insurance so they're trying to avoid mri. Is it safe for my injury to assume by touch there's no tear?

Yes and no. Acutely its very difficult to conclusively rule out everything. Initially the goal of examination and xrays is to reasonably rule out the obvious injury to ligaments and or fractures. If your pain persists for several days and or weeks then an MRI is advisable. The MRI will find the subtle stuff not necessarily appreciated on examination or xrays or it may confirm your doctors suspicions.
No. Meniscus tears sometimes are sometimes asymptomatic. But, if you not painful then with small tears the treatment is observation only. Cash prices for MRI in many places are now around $400 if you are trying to plan for it.
No. You cannot assume by touch or physical examination that there is no tear in the knee. If your knee responds to conservative therapy, and the pain resolves, you can still have a meniscal tear. Many patients have small tears which are asymptomatic. If the pain persists, then you will need an MRI.
No. A MRI will allow the physicians to identify an anterior cruciate ligament (acl), posterior cruciate ligament (pcl), meniscus tear etc. Some of these can be identified through the manipulation of the knee, but if the tear is not complete then it may not show up with manipulation. If the knee is injured and no diagnosis has been reached then proper treatment will require further imaging studies.

Related Questions

Knee injury. MRI report "PCL Avulsion fracture of tibia (6-7mm displacement) with adjacent tibial bone edema. Fibers are intact." is surgery needed?

Yes, it should if- -U expect 2 have a functioning knee 4 the rest of Ur life. It can only separate more, & a simple reduction & fixation will do what U want it 2 do, reunite the fragment 2 the tibia. The image is a tear & requires a major reconstruction if not fixed. U risk the fragment becoming a nonunion. Read more...