Unfortunately, this is a long-standing fault in the way that Illustrator's Eyedropper tool works.
To set a stroke colour based on an image, you'll need to do the following steps:
1) Make sure everything is deselected in your document, and the image you want to sample is on-screen.
2) Select the Eyedropper tool, move it over the image and click on the area you want to sample.
3) Illustrator changes the default fill colour to the one you've selected. If you don't have the Colour and Swatches panels open, do so now either from the Window menu or by selecting a workspace that contains them. (Essentials has these by default, but you'll need to click on the little << button if they're currently collapsed to icons only)
4) Click on the fill colour in the Colour panel to select it, then click and drag it to the Swatches panel.
5) Now, select the object(s) whose stroke colours you want to change, make sure to click the stroke colour in the Colour panel, then click on the sampled colour in the Swatches panel to apply it to the selected object(s).
If you're going to sample several colours from an image to use in a document, you should consider giving them appropriate names in the Swatches panel so that you can find them later. To do that, just double-click on the colour in the Swatches panel (make sure to deselect all objects BEFORE doing this!) then type a description (eg. Skintone, Aubergine, Brickwork) and click OK.