@Terry...you mean like 'bending a guitar string'?

also, trying to play a simple slow single note piece and insert the "string stretching" vibrato you speak of might work... but... when you advance to the intermediate level and start playing faster pieces, you will be able to do a 'proper' vibrato much easier and much faster than attempting to stretch or bend a string repeatedly to simulate vibrato and you will not be able to do it properly next to a string you need to move to or cross to quickly and cleanly. Sliding the string to produce this simu-vibrato will get in the way then and your progress will be stifled severely.

Learn it the right way first then you will have less to learn properly later. Start with FM's videos on finger vibrato first, then progress to the hand and then to the arm vibrato... I use a combination of all three because I'm not skilled enough yet to do just one style during my practice. In time I feel positive I will be able to train my arm and fingers to separately do what I demand of them... 

Nice Terry... LOL I started with the fingers, specifically the middle finger then the riing finger and finally the index... It's hard no doubt about it and it will take awhile, perhaps months of daily practice to get it down. Don't give up and the way I practice is just sit or kick back and play notes, make up something as you go along and hold them for a long time, make your finger vibrate as you want while doing long bow strokes.

Don't worry, at first you will have a hell of a time getting the two coordinated. I'm still having issues on occasion.

Finger first, then hand, then arm and when you start trying find a way to place the scroll of the violin against something, a desk, a wall, anything solid so you can not worry about supporting the neck with your left hand. It should just be floating out there free to move back and forth as you create the vibrato sound.