Wouldn't CALL INTERRUPT 33 also have that problem?

Call interrupt 33 with regs.ax set to 3 is what people usually use:
http://www.ctyme.com/intr/rb-5959.htm

These functions might be better:
http://www.ctyme.com/intr/rb-5962.htm
http://www.ctyme.com/intr/rb-5961.htm

http://www.ctyme.com/intr/int-33.htm

I would prefer this for QB64 mouse:

CALL _GETMOUSE(X, Y, BUTTON)
CALL _SETMOUSE(X, Y)
CALL _LIMITMOUSE(X1, Y1, X2, Y2)

Which do what they say -- get mouse cursor, set the mouse cursor and limit the mouse cursor.

On my system, I am also able to use PEN for mouse data:

PEN(n%)

�� n% An integer value between 0 and 9 that specifies what information
is to be returned about the status of the lightpen.

Argument Value returned
0 Whether pen was down since last function call
(-1 = yes, 0 = no).
1 The x coordinate of the last pen press.
2 The y coordinate of the last pen press.
3 The current pen switch status (-1 = down, 0 = up).
4 The x coordinate where the pen last left the screen.
5 The y coordinate where the pen last left the screen.
6 The character row of the last pen press.
7 The character column of the last pen press.
8 The character row where the pen last left the screen.
9 The character column where the pen last left the screen.
�� The lightpen coordinate system is identical to the current graphics
screen mode, without viewport or window considerations.