The extremely hot and tenuous accretion flow in the immediate vicinity of Sgr A* is believed to be invisible (too dim) in the X-ray band, except for short X-ray flares. Here we point out that during pericenter passages, close brightest stars irradiate the inner region of the accretion flow, providing a plenty of optical/UV photons. These seed photons are Compton up-scattered by the hot electrons of the accretion flow to higher frequencies, some into the X-ray band, potentially making the innermost accretion flow much brighter in X-rays than usual. We propose to use coordinated near infra-red and X-ray observations of close star passages to put constraints onto Sgr A* accretion theories. The absence of a noticeable change in the steady emission of Sgr A* as observed by Chandra in the year 2002, when the star named S2 passed through a pericenter of its orbit, already rules out the hotter of the "standard" Advection-Dominated Accretion Flows. The less dense accretion flows, in particular the model of Yuan et al. (2003), passes the test and is constrained to accretion rates no larger than similar to few x 10(-7) M. year(-1).