Altium doesn't let me place components the way I want
Give this a try:

Go to your DXP menu --> Preferences, expand "PCB Editor" in the left pane, and select "Interactive Routing". Under the "Dragging" heading, make sure "Component pushing" is set to "Ignore" instead of "Avoid". 



When set to "Avoid", I believe this rule follows your component clearance rules and does not allow you to place a component within that clearance (near another component).