Seem to me that a random small stroke across an image would be going over many colors bigger tips more colors which color would be your color match? I would think that pointillism may be possible not a Rembrandt.
Are you sure Corel Pinter does not add brush strokes textures to existing colors a distort displacement.
This is how auto-painting works in Corel Painter. The brush picks up the color underneath it at the starting point of the stroke. It tends to look better if it's a mixer-type brush, which will smear colors and create some brushstroke detail. Kind of impressionistic I think. The final result, depending on the parameters and brush type, is very useful as an image that can be used or recombined with other images, or further processed.
Photoshop "mixer" brushes work very much like wet brushes in Corel Painter. If a PS plugin could use the mixer brush to paint, the result would be quite interesting.
I don't know of a plugin that will simulate a painting. There may be an Action that will try to do this but I don't know of one. There are of course standalone programs that aim to do this.
But Photoshop offers various ways to simulate natural media. It all depends what you mean by "painting". You need to have an idea what - what style of artwork - you are aiming for. So, you can use the Art History Brush to make both loose and detailed watercolours and oils, the Mixer Brush can clone Smeary Oil brushstrokes, the Pattern Stamp Tool for detailed oils and watercolour washes, and the Smudge Tool to make highly detailed softened brushstrokes. Then there are chalks for pastels, and filters for pen and pencil outlines used in combination to produce mixed media effects like pen and wash. All of these work from a photograph.
Here is quite a nice technique using the Art History Brush:
These may involve more work than you want to put in but the results can be quite good.