With a stat like "less than 1%" the order of magnitude is at least 1/10 of 1% otherwise it's an invalid format for a statistic, it's also most likely >= 0.5 because of rounding... 0 is also less than 1 so with your logic the statistic is meaningless.
Yes, all "X is less than Y" statistics are meaningless unless there the convention you mention is strongly held by journalists when they interpret studies - which is unlikely.
i.e. it'd be very easy for a study to say "we have shown that it's likely that the effect size is less than 1%" and then a journalist to interpret that as <1%, and then for a reader to incorrectly think "they wouldn't have said this if it were actually 0.1% or lower".
