I think it might be beneficial to see the actual context in which the comments were made (by me; not as a referee, but just someone that Jim wrote to and asked for comments on his nice paper, which by the way, has a fair bit of its provenance in various MO threads).

The work in question is on the arxiv here. Various properties of an ordered field $R$ are being considered and compared. The last two are:

(17) The Shrinking Interval Property: suppose $I_1 \supset I_2 \supset \ldots$ are (bounded) closed intervals in $R$ with lengths decreasing to zero. Then the intersection of the $I_n$'s is nonempty.

and

(18) The Nested Interval Property: Suppose $I_1 \supset I_2 \supset \ldots$ are (bounded) closed intervals in $R$. Then the intersection of the $I_n$'s is nonempty.

I was not thrilled with the use of (bounded) in (17), but I let it go. I objected to the use of (bounded) in (18).

Note that "(bounded)" is playing different roles in the two statements. In (17), it is a superfluous hypothesis: if the lengths of the intervals are decreasing to zero then necessarily all but finitely many of them are bounded. In (18) it certainly isn't. I found this lack of parallelism especially confusing: so confusing that the first time I read it I honestly did arrive at the (ridiculous) conclusion that Jim Propp was unaware that e.g. $\bigcap_{n=1}^{\infty} [n,\infty) = \varnothing$.