Wash-out periods are periods without treatment between cross-over trials to minimize carry-over between the trials.
What the quoted discussion is talking about is a run-in period, where participants either given placebo or active treatment prior to the study with the intention of excluding non-compliant participants or participants with intolerable side effects.
Run-in period: A period before randomisation when participants are monitored but receive no treatment (or they sometimes all receive one of the study treatments, possibly in a blind fashion). The data from this stage of a trial are only occasionally of value but can serve a valuable role in screening out ineligible or non-compliant participants, in ensuring that participants are in a stable condition, and in providing baseline observations. A run-in period is sometimes called a washout period if treatments that participants were using before entering the trial are discontinued.
In the acupuncture trial, a three-week 'washout' period was built into the trial between the two treatment periods. This is a common method to minimize 'carry-over' effects and ensure the participant is in the same state at the beginning of each period, though it is not always sufficient.
Many cross-over trials include a period between interventions known as a washout period as a means of reducing carry-over.
Effect on external validity
Pre-randomisation run-in periods are also often used to
select or exclude patients. In a placebo run-in, all
eligible patients receive placebo and those who are
poorly compliant are excluded. There can be good
reasons for doing this, but high rates of exclusion
will reduce external validity. For example, one trial of
the effect of salts on blood pressure excluded 93% of
patients in a placebo run-in period. Active treatment
run-in periods in which patients are excluded if they
have adverse events or show signs that treatment may
be ineffective are excluded are more likely to undermine
external validity. For example, two RCTs of
carvedilol, a vasodilatory blocker, in chronic heart
failure excluded 6% and 9% of eligible patients in
treatment run–in periods because of worsening
heart failure and other adverse events, some of which
were fatal. In both trials, the complication rates in the
subsequent randomised phase were much lower than
in the run-in phase.
So, yes, run-in periods that exclude a high number of participants have lower external validity.
How to account for this when reading or doing research
See (Berger and Durkalski) and (Brittain and Wittes).
The effect of run-in periods on research simply changes how we should expect the results of these studies to transfer to practical treatment. In the case of compliance-based exclusion, a follow-up pragmatic study (Roland and Torgerson) would reveal the discrepancy. In the case of exclusion based on adverse effects, sometimes that test-dosing is reported. While the external validity of the eventual study may be lessened, good studies will make this limitation clear, describe the demographics of the selected participants, and provide details about the pre-trial exclusion. Be alert for large numbers of unexplained pre-trial exclusions.
Berger, Vance W., and Valerie L. Durkalski. "Run‐In Period." Wiley Encyclopedia of Clinical Trials.
Brittain, Erica, and Janet Wittes. "The run-in period in clinical trials: the effect of misclassification on efficiency." Controlled Clinical Trials 11, no. 5 (1990): 327-338.
Roland, Martin, and David J. Torgerson. "Understanding controlled trials: What are pragmatic trials?." Bmj 316, no. 7127 (1998): 285.