You say "engine mounts"? Did you mean struts? If so, the mechanic is right,
the upper mount should hold the strut ball-bearing very firmly. Over years
of driving, the upper mount which is essentially a neoprene or rubber-like
donut shaped thing, no longer holds the bearing which allows the strut to
rotate as the steering wheel is turned, firmly. This causes the strut to
move sideways causing increased negative camber and if really badly worn, it
causes changes in camber of the road-wheel a the car travels around a bend.
I've experienced this in a Volkswagon Passat. Also, its likely, as the car
goes over more severe mounds in the road-surface, that noise will come from
the upper mount as the bearing slaps around in the worn rubber support. The
mechanic simply demonstrated the vertical wear, by jacking up the car so the
wheels were off the ground,..this would cause the strut to rest at the
bottom of the play in the mount, then as weight is re-applied to the strut
as the wheels touch the ground, the strut moves upward within the play or
slop in the upper mount.

Jason

If the bearing separates from strut mount, the whole strut assembly will
fall off, if the ball joint to steering knuckle bolts are removed.
Usually the rubber cracks between the molded in bearing and the outer
flange with three mounting studs. This problem is common on all
Cressidas and even on 96 Mazda Protege, I haven't see this problem on
late 80th Camrys.
The mounts are rubber and some movement is normal. If they are worn the
noise will be  most heard as suspension buttoms. The most common causes
for negative camber are the worn lower control arm bushings. Poor
installation methods such as hammering on the axleshaft for removal may
damage bearings in the hub/ differential causing hum/growl which is
speed related. I personally do not think that the upper strut mounts
are bad.