You can have a short squeeze without naked shorting. Shorts who aren't naked have borrowed the stock from someone. If that person asks for it back, they have to go out and buy it in order to return it.
At least in theory, if retail investors buy up the stock, some of the institutional investors who own it, and who have lent it out, will sell it to them. This could mean that they recall lent stock. As this happens, shorts might have to compete to buy the stock. Equally, as the price gets higher, shorts might have to cut their losses, which also means buying back the stock. If the people buying it now don't sell it and don't lend it they will withdraw a lot of the supply.
At least in theory, if retail investors buy up the stock, some of the institutional investors who own it, and who have lent it out, will sell it to them. This could mean that they recall lent stock. As this happens, shorts might have to compete to buy the stock. Equally, as the price gets higher, shorts might have to cut their losses, which also means buying back the stock. If the people buying it now don't sell it and don't lend it they will withdraw a lot of the supply.