Just going to throw out some very broad level stuff here due to not having the kind of information and data required to really apply some specificity to the subject.

Low intensity recovery exercise 1-4 days post-intensive-exercise can assist in the combating soreness as well as the loss of joint ROM (Range of Motion) and stiffness; the improved blood flood can also help by hastening the removal of metabolites. Debatable whether it assists with the repair of damaged muscle fibres, muscle hypertrophy, or the laying of new fibres beyond any benefits improved blood circulation may bring.

Also, interesting to note that initial strength gains can be the result of more efficient muscle (motor unit) recruitment and co-ordination on a neural level.

Curiously, do you have muscle soreness and\or muscle stiffness\loss of joint ROM 12-48 hours after an intensive training ride? If so, in combination with the experienced muscle weakness and two days required to return to maximal strength, that could be DOMS (Delayed Onset Muscle Soreness). Plenty of strategies to tackle muscle soreness but not so many scientifically proven recovery strategies for the muscle weakness, perhaps compression but it needs further investigating.

It is more prominent in exercises which feature eccentric contractions - such as the lowering phase of the Biceps Curl - but it can also be brought on by unaccustomed activity, such as a higher intensity, or resuming an activity after an extended period of inactivity.

If you can you should certainly try mixing in some recovery rides in to your R&R (rest and recovery) and see how it works out for you. It is worth remembering the Principle of Individuality, which says that training needs to be tailored to the individual. Due to differences in fitness levels and other factors what works for one individual isn't necessarily suited to the other, something to note if the cyclists at the club are better conditioned and aren't tailoring advice to lower fitness levels.

Overtraining can occur due to not letting the muscle tissue recover sufficiently in between intensive workouts; so until the body adapts to the stresses being placed on it is probably better to build up from two days of R&R. Consider whether you are overloading your body too quickly; can you lower the workload of each session, ease the R&R required to just one day and add in an extra session in the week?

At a very general level a resistance program that aims to build muscular strength, power or endurance, assuming a stimulus for adaption is present, does between 3-4 sessions a week to ensure progression occurs. On a very general level 1-2 sessions is often too little and 5-6 sessions impacts R&R and gets in to overtraining territory.