Well, if the external clock is connected to a regular non-clock input pin then AFAIK the rest of his argument is rubbish. You can connect the input from the non-clock input to a global clock net, but then the damage is already done (clock skew). That said, if you run that crappy clock input to a PLL, and then let the VCO essentially clean things up for you then you maybe can get away with it. But then again you would probably need a feedback path, and I vaguely recall that only worked well for dedicated clock pins.
Sounds like the PCB guy doesn't want to reroute the clock signal, and his subconscious is generating BS arguments to support his conscious need for NOT WANT REROUTE GNNN.
Anyways, the dedicated clock pins have predictable low delays. Generic fabric will have higher variability in delay. For low speed you can probably get away with it, for high speed not so much. And that < 100 MHz clock probably still is low enough that you can get away with it, but don't quote me on that.
Basically it comes down to cost of rework. Either you reroute inside the fpga fabric, or on the pcb. If rerouting the clock signal on the pcb turns out to be really difficult because of whatever reason, then essentially rerouting it inside fpga fabric may be acceptable.
As a general policy however I'd say try to aim for that dedicated clock input next time when routing a board.
Also, the timing analysis tools will have better known delays for that dedicated clock input making timing analysis easier.
So in short: will probably work, makes timing analysis a little harder.