Many of the low volume or high intensity styled programs make claims about diminishing returns from extra work. The easiest way to address this question is to look at the science of training volume. I agree with one of the commenter's (Dave) that exercise science is not always a solid science, but his recommendation replaces measurement with opinion.
Volume vs HIT: The Answer
There have been many studies that have sought to understand whether it is better to use a single set, many sets, how many sets, etc. Most of the training programs used by athletes today are based upon periodized programs developed by the former eastern block Olympic coaches. But there are two issues: strength and hypertrophy.
Firstly a strength training meta-analysis by James Krieger (Journal of Strength & Conditioning Research. 23(6):1890-1901, September 2009) found that 2-3 sets led to 46% greater strength gains than 1 set.
There has been considerable debate over the optimal number of sets per
exercise to improve musculoskeletal strength during a resistance
exercise program. The purpose of this study was to use hierarchical,
random-effects meta-regression to compare the effects of single and
multiple sets per exercise on dynamic strength. English-language
studies comparing single with multiple sets per exercise, while
controlling for other variables, were considered eligible for
inclusion. The analysis comprised 92 effect sizes (ESs) nested within
30 treatment groups and 14 studies. Multiple sets were associated with
a larger ES than a single set (difference = 0.26 +/- 0.05; confidence
interval [CI]: 0.15, 0.37; p < 0.0001). In a dose-response model, 2 to
3 sets per exercise were associated with a significantly greater ES
than 1 set (difference = 0.25 +/- 0.06; CI: 0.14, 0.37; p = 0.0001).
There was no significant difference between 1 set per exercise and 4
to 6 sets per exercise (difference = 0.35 +/- 0.25; CI: -0.05, 0.74; p
= 0.17) or between 2 to 3 sets per exercise and 4 to 6 sets per exercise (difference = 0.09 +/- 0.20; CI: -0.31, 0.50; p = 0.64).
There were no interactions between set volume and training program
duration, subject training status, or whether the upper or lower body
was trained. Sensitivity analysis revealed no highly influential
studies, and no evidence of publication bias was observed. In
conclusion, 2 to 3 sets per exercise are associated with 46% greater
strength gains than 1 set, in both trained and untrained subjects.
Now the low volume claims are for diminishing returns after the first set. This is clearly not the case, but there is a point that no more strength is gained (4-6 sets) by performing more work. I won't address it here, but it is to do with how fast the body can restore ATP and how much micro-trauma has been induced.
Hypertrophy is the second part of weight training. Krieger again performed a meta-analysis of the research (Journal of Strength and Conditioning Research: April 2010 - Volume 24 - Issue 4 - pp 1150-1159) and found that increasing the number of sets increased the amount of hypertrophy by 40% (up to 6 sets).
Previous meta-analyses have compared the effects of single to multiple
sets on strength, but analyses on muscle hypertrophy are lacking. The
purpose of this study was to use multilevel meta-regression to compare
the effects of single and multiple sets per exercise on muscle
hypertrophy. The analysis comprised 55 effect sizes (ESs), nested
within 19 treatment groups and 8 studies. Multiple sets were
associated with a larger ES than a single set (difference = 0.10 Â±
0.04; confidence interval [CI]: 0.02, 0.19; p = 0.016). In a dose-response model, there was a trend for 2-3 sets per exercise to be
associated with a greater ES than 1 set (difference = 0.09 Â± 0.05;
CI: −0.02, 0.20; p = 0.09), and a trend for 4-6 sets per exercise to
be associated with a greater ES than 1 set (difference = 0.20 Â± 0.11;
CI: −0.04, 0.43; p = 0.096). Both of these trends were significant
when considering permutation test p values (p < 0.01). There was no
significant difference between 2-3 sets per exercise and 4-6 sets per
exercise (difference = 0.10 Â± 0.10; CI: −0.09, 0.30; p = 0.29). There
was a tendency for increasing ESs for an increasing number of sets
(0.24 for 1 set, 0.34 for 2-3 sets, and 0.44 for 4-6 sets).
Sensitivity analysis revealed no highly influential studies that
affected the magnitude of the observed differences, but one study did
slightly influence the level of significance and CI width. No evidence
of publication bias was observed. In conclusion, multiple sets are
associated with 40% greater hypertrophy-related ESs than 1 set, in
both trained and untrained subjects.
So there is no science to support the claim that doing more sets will only see small increases in returns. It is possible the person making this claim has not understood the conclusions of studies such as the ones I have cited, but it is more likely that the claims are unfounded.