Charles - you're right. The meat tissues admit the liquid injection just fine, but it's those same meat tissues that help act as a barrier and plug up the needles.
I've found that is I pull the needle out as I inject this simple action helps leave behind a trail of savory bits. That method still isn't perfect.
What I generally do now is use a paring knife to poke holes in the meat itself and then I use my fingers to push a paste of all the savory bits into the meat. That works better than anything I've found. It works really well with garlic cloves, green onions, rosemary, thyme, peppers, etc.