To quote Frank Day: ugh. What a crappy study - [of course two different measures of training load calculated from the same (heart rate) data will be correlated with each other. The only way you wouldn't see such auto-correlation would be if the data were manipulated in radically different ways.

If you're looking for a study validating TRIMP (as a predictor of physiological strain), these are probably as good as it gets:

Busso T, Hakkinen K, Pakarinen A, et al. A systems model of training responses and its relationship to hormonal responses in elite weight-lifters. Eur J Appl Physiol 1990; 61: 48-54.

Busso T, Hakkinen K, Pakarinen A, et al. Hormonal adaptations and modelled responses in elite weightlifters during 6 weeks of training. Eur J Appl Physiol 1992; 64: 381-386.

Even then, though, you can't really separate the validity (value?) of TRIMP as a predictor of physiological strain from the impulse-response model itself, since they didn't look directly at the relationship of TRIMP to hormonal response (e.g., during/after a single bout of exercise).

Anyway, back to TSS: when I first proposed it back in 2003, it was the first ever objective, stress (i.e., input)-based measure of training load, with its purpose being to serve as input function when modeling the relationship between training and performance. Despite regular encouragement from me, the scientific community has unfortunately been quite slow to get around to studying the idea (there are reasons for that, but no time now to explain). A decade or so on, though, things are starting to change. Specifically, in addition to Fergie's quite-commendable effort several other abstracts/papers have utilized/assessed TSS and/or one of its progeny/imitators/components (with Phil Skiba leading the way back in 2007):

Skiba PF. Evaluation of a Novel Training Metric in Trained Cyclists. Med Sci Sports Exerc 2007; 39: S448.

(See below.)

http://www.ncbi.nlm.nih.gov/pubmed/19910822

(Demonstrates that rTSS/the PMC can be used to predict running performance.)

http://www.ncbi.nlm.nih.gov/pubmed/20058020

(Demonstrates that variations in TSS/CTL predict variations in Hb mass.)

http://www.ncbi.nlm.nih.gov/pubmed/21113616

(Used TSS and IF to match/compare the training of two groups of cyclists)

http://www.ncbi.nlm.nih.gov/pubmed/24405984

(Demonstrates that the running equivalent of normalized power is a predictor of optimal pacing strategy.)

http://www.ncbi.nlm.nih.gov/pubmed/24104194

(Demonstrates that the running equivalent of TSS is a better predictor of training-induced improvements in performance than either TRIMP or Foster's session RPE.)

Of the above, Phil's original study is probably most directly on-point, so it is probably worth reproducing the abstract here (with some emphasis added):

"Numerous systems have been developed to quantify athlete training, many based upon subjective criteria. Recently, a novel system based upon lactate-normalized power output has been popularized for cycling (Coggan 2003, 2006), which has not been evaluated in the literature. This system should be superior to existing methodology because it relates a purely objective parameter (power output) to resultant metabolic stress by weighting cyclist power output with a 4th power function that closely tracks serum lactate response to a standard ramp exercise protocol. This value is then compared to the average power an athlete is capable of maintaining for one hour (previously shown by Coyle et al (1988) to be highly correlated to power output at LT) to generate a training stress score.PURPOSE: This investigation examines the validity of this algorithm in a group of trained cyclists (n=5). This work also evaluates the utility of the related training stress scoring system in the quantification of training load and performance modeling using convolution integrals.METHODS: Power meter files for one-hour (range 51–62 minutes) individual time trial races (ITT) and one-hour (range 51–60 minutes) criterium races (CRIT) were obtained from 5 trained cyclists. Average power (AP) values were compared between ITT and CRIT. CRIT power data were then subjected to a 4th power-weighted 30-second moving average to generate a normalized power (NP) value. ITT AP and CRIT NP were then compared. Training stress scores were generated and used as the input function for systems-based performance modeling for a national-level track cyclist per the method of Morton et al (1991).RESULTS: CRIT AP was highly correlated with ITTAP (p<0.04, r2=0.791), however, CRIT NP was more highly correlated to ITT AP (p<0.001, r2=.978). Using the examined training stress score, it was also possible to accurately model performance (p<0.0001, r2=0.9189). CONCLUSIONS: Though additional work with a larger sample size is required, these data indicate that NP may be superior to AP in describing how strainful a variable-power work task is. These data also demonstrate the utility of the associated training stress quantification system in performance modeling for trained cyclists."

In addition to the above, a number of other peer-reviewed studies have also used, or at least cited, some of my other ideas, e.g.:

Abiss CR, Quod MJ, Martin, Netto KJ, Nosaka K, Lee H, Suriano R, Bishop D, Laursen PB. Dynamic pacing strategies during the cycle phase of an Ironman triathlon. Med Sci Sports Exerc 2006; 38:726-734.

Gregory CM, Doherty AR, Smeaton AF, Warrington GD. Correlating multimodal physical sensor information biological analysis in ultra endurance cycling. Sensors 2010; 10:7216-7235.

Francis JT Jr, Quinn TJ, Amann M, Laroche DP. Defining intensity domains from the end power of a 3-min all-out cycling test. Med Sci Sports Exerc 2010; 42:1769-1775.

Robinson ME, Plasschaert J, Kisaalita NR. Effects of high intensity training by heart rate or power in recreational cyclists. J Sports Sci Med 2011; 10:498-501.

Cowell JF, McGuigan MR, Cronin JB. Movement and skill analysis of Supercross BMX. J Strength Cond Res Publish Ahead of Print 2012 (DOI: 10.1519/JSC.0b013e318234eb22)

Note that there may be others out there, since as merely a hobbyist in this arena I don't make a practice tracking each and every citation of my work...