The person who enjoys solitude may still appreciate an invitation offered without assumptions.

Liking your own company is not the same as wanting to be forgotten. What makes an invitation heavy is usually the pressure attached to it: the assumption that a no means something, or that it will need explaining. Take that away and the same invitation is simply a good thing to be handed. Being thought of matters even on the evenings you would rather stay in.

Keep inviting the quiet people in your life, and make declining cost them nothing. Say that either answer is fine and mean it. If you are the one who usually stays in, try saying no without the paragraph of justification.