Unless their comments on that subject are limited to figured caps and/or veneers, this is your first indication that this particular group of people knows absolutely nothing about a guitar. While a figured top has a distinct effect on the acoustic tone of an electric guitar, the effect on the amplified tone depends largely on the thickness of the top, with the amount of wood in contact with the bridge being the primary factor there. A hardtail or v-trem sits flat on the figured top, while the inserts for a tuneomatic rest mostly in the core body wood, not the cap, and as long as the bridge does not rest directly on the cap, the core body wood will be the determining factor.
A pickup is not a microphone, and thus cannot detect vibrations from the wood, ergo the method of mounting is irrelevant to the end-result. The only thing direct-mounting can possibly do is add mass to the body, or to be more specific, act as a substitute for the wood removed for the pickup cavity. In blueman335's example, adding wood shims to the pickup cavity to set the pickup at the desired proximity to the strings resulted in filling in the hole with wood AND adding a pickup, and the total mass of those shims and pickup were at least equal to, but more likely greater than, the mass of the wood removed to make the cavity in the first place.
As the string vibrates, the wood resonates. A truly solid-body guitar - one that has no cavities for pickups or controls - will resonate differently before it is routed for pickups, even if those cavities are just big enough to hold the pickup. When the cavity is routed, there is a loss of connection between the wood on either side of the cavity.
By direct-mounting a pickup, the pickup acts as a prosthesis for the amputated wood, transferring the resonance to the body rather than it being diminished by the empty cavity as is the case of a ring/guard-mounted pickup.
However, the pickup takes no notice of this directly, no matter how it's mounted, as it is focused by design only on the strings.
If one were to build a completely solid guitar with no cavities and mount a pickup on an external frame that suspended the pickup over the strings in the correct position (i.e. as it would be were it mounted in the guitar), with the frame not touching the guitar in any way, the amplified result would be considerably different than when the body was routed to fit the pickup.