wrote:

That phrase is printed on both the cover and on the
coupon inside the voucher, signed and stamped by the Continental gate
agent.

The voucher also states inside the front cover and on the coupon
itself, “This certificate is valid for a First Class upgrade when
traveling on a paid fare ticket

It is good "on a paid ticket", not all paid tickets.
Was there anything else on it, such as "some restrictions apply"?
I would expect limitations on free upgrades and tickets received in this
manner, which is why I prefer $$$ vouchers.

I don't understand the comment regarding BusinessFirst. I don't think CO
flies BF to Barbados, do they? Like other airlines, I suspect this
might be Business class, as other airlines tend to call it businss class
on international flights in standard domestic first class seating to
indicate this is not an "international" first class flight.