I was about to post that this is indeed still the case today, but just as well I checked....
When I was going through tank school, many moons ago, FM 17-15 still ruled. This is the 1996 version. http://www.bits.de/NRANEU/others/amd-us-archive/FM-17-15%2896%29.pdf In it are a list of tactical mission tasks a tank platoon may perform, and it was to be noted that tasks such as "Secure" "Retain" and "Clear" were not on that list (There is an overall list of tactical tasks in doctrine. Infantry can do them all). I do note that the current manual, ATP 3-20.15 https://fas.org/irp/doddir/army/atp3-20-15.pdf does include these tasks. Therefore somewhere in the last ten years since I effectively got out of the tanking business, there has been a change. However, The Face of Battle was written some 40 years ago, and so this recent change certainly does not apply with regards to the accuracy of his writing at the time, at least as far as the US Army was concerned.
Especially with the basic equipment found on a tank up until the 1980s or so, it would be basically impossible for a tank (or other AFV) to do everything the infantry could do. A tank unit could almost certainly secure an asphalt parking lot, and maybe a piece of (flat) desert, but that would be about it. Start putting terrain features into the mix, given we tend not to fight over parking lots and empty desert, things like buildings, bunkers, gulleys, sewers, caves, tunnels, creeks, woods etc and all of a sudden the task of the tank becomes very difficult. One can certainly clear a building in a tank, but the building won't be standing at the end of it. Good luck clearing a sewer main. An infantry unit could almost certainly sneak up on a tank unit, especially at night in the real world, by use of concealment by vegetation, elevation differences, etc. When a tank unit attempts to take ground, how does it check for booby traps, mines, tunnels, and so on? These are the things which only infantry can do effectively. So, it was drilled into us, only Infantry units can take and hold ground.
Why the recent change? The Powers that Are have not deigned to inform me, but I can hazard two guesses.
The increase in capabilities of tanks. With thermal imagers, the old sneaky techniques infantry could use no longer particularly work. Vegetation and darkness no longer provide concealment. (Seriously, in training we'd let the infantry get very, very tired crawling up closer to us before finally putting them out of their misery.) Of course, it still requires attentive tankers, if they're looking the wrong way, they won't catch 'em.
We don't like to admit it, but these days us tankers are spending a lot of time outside of our tanks pretending to be infantry. (Dragoons, the Army has decided to call this function). The days of a tank crew being equipped only with personal defense weapons (Sidearms and the odd grease gun) are long gone, we're as festooned with weapons and ammo as the typical rifle team. It makes a lot of sense for the Tank Platoon manual to be re-written to assume that we are on foot as well as on the tank.