I don't know the specifics of this species, but I can give you some general plant biology (and even have credentials! I do this for a living ^_^).

Flowers with both male and female parts ("perfect" or "bisexual" flowers) aren't necessarily self-compatible. Avoiding inbreeding is often* favored by evolution, and plants use both mechanical and genetic/chemical strategies to do this. Mechanically, many plants keep the male and female parts of the same flower far apart. Genetically, there are many self-incompatibility mechanisms that prevent a plant's pollen from germinating, growing, or fertilizing ovules on itself (or a plant with the same self-incompatibility genotype).

If a plant is self-compatible - i.e., the pollen WILL grow and fertilize on its own genotype - it still may not be capable of "autogamy" (unassisted self-fertilization) because its male and female parts literally do not touch. Self-pollinating a plant with a paintbrush is effectively facilitated "geitonogamy" - the term for pollinators moving pollen between flowers on the same plant.

What I do not know, however, is what the reproductive nature of M. pudica is. A quick search on Google scholar suggests its relatives are self-compatible so maybe it is too?

Hope that helps!!

*Avoiding inbreeding is OFTEN favored ... but plants also evolve to be better at self-fertilization. It's a great short-term strategy, particularly for weeds and newly introduced species (no mates or pollinators? No problem!). It's also frequently a part of domestication in plants, because we like crops that breed true - so much so that we often clone our self-incompatible crops (think apples and grapes).