It all depends on the controller chip and layout of the connections in the keyboard, I think the issue with USB keyboards was that in the early days especially some manufacturers used to use skimp a bit.
It's actually all down to the way the keyboard keys are hooked up to the controller, as it's done (from memory) in grids with different keys in different connection grids, and the problem comes when more keys on the same "grid" (usually ones near each other) are pressed than the controller allows (the way to work round that is to have keys that are commonly pressed together on separate grids as much as possible, or a better control chip).
The problem is, having more of the connection grids, and a better chip adds to the manufacturing price, so the cheapest boards tended to be optimised for normal windows usage where you might only have say 2 of modifier keys (ctrl, alt etc) and one or two of the normal keys pressed at once - not good for gaming where you might have ctrl, space, w and a pressed together to do a crouching diagonal strafe.
IIRC most keyboards, even the cheapest can usually take 3-4 keys together, some can take several more but dependant on which ones exactly.
Keyboards sold as "gaming" or higher priced ones are usually optimised to allow the most keypresses possible, taking into account not just normal use but the commonly used keys for games (things like WASD, shift, ctrl, alt and space) and have the electrical connections wired up to allow for them to be pressed in combinations of 3-4 at once.
The Mouse thing was certainly true back in the early days of USB1, and I think even today potentially if you're using the mouse on the same USB controller as say an active USB HDD or similar bandwidth hog (all devices on the same controller share the bandwidth), but not if you either use the controller just for the usb keyboard/mouse or with other low bandwidth things (like game pads etc).
Sorry if my explanation is vague, i'm rather tired
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I don't think I've ever had any issues with any of my keyboards, but I don't think I've ever used the absolute cheapest ones for any serious gaming.