Interesting study but there are important notes to mention:
1. HF HRV is not an index of cardiac vagal "tone" since it can be hugely changed by respiration frequency with no change in average HR (mean RR-interval). The gold standard in physiological studies for cardiac vagal "tone" is the average HR (mean RR-interval). That pharmacological blockade decreases HF HRV does not mean that it can represent tonic activity since blockade attenuate both tonic and phasic outflow. Therefore, referring to HF HRV as cardiac vagal "tone" is not correct. HF HRV represents respiration-related cardiac vagal outflow and this is very important to consider since this study is about central modulation of HRV. Both interventions in this study could affect respiration parameters. Respiration rate and depth (tidal volume) has considerable impact on HRV, especially frequency domain indexes. Without appropriate evaluation of respiratory parameters it would not be clear how interventions could affect HRV, via which mechanisms? I would suggest to also look at other indexes of HRV, like mean RR-interval which is more valid index of cardiac vagal "tone" and RMSSD which is assumed to be less affected by respiration.
2. It's very important to be aware that the LF HRV is not a valid index of sympathetic tone. Authors have cited the old task force paper (1996) while later studies have repeatedly shown that LF is also under influence of vagal activity: for review Exp Physiol. 2011;96(12):1255-61 and Psychophysiology. 2013;50(5):477-87. Valid evaluation of sympathetic activity can be achieved by measuring muscle sympathetic nerve activity.