OT: Wireless Network Strength Dependent On Wired Network?

[Neil <kngspook () gmail com>]

Okay, a small, offtopic question. (I figured you guys were a far more
reliable source than my local ${electronics_store} salesperson...)

Consider the following setup:
internet pipe -> wired network -> (wireless router) wireless network ->
computer1, computer2

Suppose the signal coming in on the pipe is good, but the signal
deteriorates rapidly in wired network (old & bad wiring). Now, the two
computers are connected via the wireless network only. computer1 has a great
connection (it's in the same room as the wireless router), but computer2 is
far away and drops the wireless connection frequently.

Now, a former electrical engineer is claiming that if we improve the wired
network so that the signal comes across better, then computer2 won't drop
the wireless connection so frequently. (He says that the signal emitted by
the wireless router will be improved by feeding it a better source signal.)

I argue that there are two separate signals: the internet connection signal
coming in on the pipe, and then the wireless network signal being emitted
from the wireless router; and their strengths are independent. In other
words, if we improve the wiring, the wireless signal will not get any
stronger.

So...basically, who's right? (Or are neither of us?) Any thoughts, comments,
corrections?