Well, there is "textual evidence" making these claims (such as Polybius describing the Seleucid elite fighting in Roman fashion) [Polybius 30.25.3], however it is rightly questioned, as (at least generally) the tactics and equipment of Roman legionaries were not especially unique - Celtic peoples often wore similar equipment (indeed, the gladius Hispaniensis and the Scutam shield were both adapted from armaments used by the Celt-Iberians). [http://www.ancient.eu/Gladius_Hispaniensis/], [https://books.google.com/books?id=X_aoHLV02DAC&pg=PA109&lpg=PA109&dq=scutum+shield+iberian&source=bl&ots=OOZF3LOQ6L&sig=1LRrucqjQl3sUAwnDWGLksDUsX8&hl=en&sa=X&ved=0ahUKEwiSmJ6h5p7PAhUBXh4KHVvMB_QQ6AEIVTAO#v=onepage&q=scutum%20shield%20iberian&f=false]

Others, like Mithradates Eupator VI of Pontus (the Greatest) actually did take on Roman turncoats (specifically from the Roman Civil Wars that occurred during his reign) to train their armies, and so could properly be said to have adopted their tactics after the fact (though Galacian soldiers, again, fought in a similar fashion already). [Plutarch, Life of Lucullus 7.4].

(Sorry if the formatting is wrong - I don't know how to do all of this fancy "link embedding" on reddit. Just Italics and Bolding.)

Regarding the 'imitation' legionaries of the Pontic and Selucid armies in the 2nd and 1st centuries BC, /u/MithradatesMegas does a fine job of outline some of the literary evidence. He also makes a very good point regarding the fighting style of Roman legionaries, which was not peculiar only to the Romans, that I would like to expand on slightly.

To put it simply, the infantry tactics of Roman sub-units, that is to say their "fighting style", was characterised as a relatively loose formation of infantry fighting with throwing spears and spear/sword and shield in close combat. Extra space was required for the proper use of sword and shield as opposed to a much tighter phalanx formation where the proximity of men, shields and spears gave the formation its mass and staying power. This was the Greek and, as a result of Hellenisation, also the Eastern heavy infantry tradition. By contrast, the Romans, Samnite, Etruscans, Iberians, Celtiberians and other Western Mediterranean peoples used the looser, more individual-combat oriented sword/board/throwing spear style of combat that basically formed a 'Western Mediterranean' fighting style.

Hannibal's Iberian troops in the Second Punic War, as experienced troops that Hannibal had provided with further training and a product of this 'Western' fighting style, were essentially proficient in the same tactics as the Romans. As /u/MithradatesMegas has said, they also used functionally the same equipment.

Polybius also notes (3.114) that Hannibal's Libyans, professional close-order spearmen who were perhaps his best troops, had by the Battle of Cannae also been equipped with Roman armour. However, the Iberian infantry in particular were functionally quite similar to Roman infantry. This remained the case in the Iberian wars that following Rome's annexation of Spain, though Iberian troops perhaps fought in even looser order than the Romans at times.

As such, through the examples of 'imitation' legionaries of Mithridates, Antiochus and the 'Western' style heavy infantry of Iberia and Italy, Roman legionaries were not the only exponents of their individual methods of fighting and associated types of equipment. What Romans did do that their opponents did not was train and drill more and work under a very strict and effective system of discipline, tactics and command that, aside from their dress, made them distinctive on the battlefield. While the individual fighting skills of legionaries could easily be found in warrior peoples, and their equipment was not particularly distinctive only to the Romans, the organisation and discipline of Roman armies, as well as their sheer number and material resources, was what really marked them out from any 'imitators'. The human and logistical resources of Mid-Late Republican Rome were incomparable to any of their foreign rivals, and the organisation, discipline and training of their army was to an extent the product of hundreds of years of development and military experience that could not be replicated by their enemies, who generally lacked the collective technical expertise of Roman officers. As such, by merely adopting Roman-style dress and equipment, Mithridates and Antiochus were somewhat missing the point of what made Roman soldiers so effective.

As for the Gauls and Germans, from the Late Republic onward they certainly did begin to adopt Roman tactics where possible, though their general inability to win pitched battles by the 1st century BC made it hard for them to acquire much Roman equipment or acquire any sort of 'institutional' technical military skill. Caesar makes comment of the Gauls' impressive capacity to adopt Roman military techniques (Caes. BG 7.22) and implies a significant increase in Gallic military sophistication (7.34-5) during the course of the Gallic campaigns (cf. 2.10-2), though of course Caesar's own skills also increased dramatically (compare his being surprised in 2.19-20 to the complexity of his leadership at Alesia, for more see Kagan 175-7, 190). The introduction of Gauls and Germans into the Roman army in the Imperial period further blurred the lines, with Arminius' successful ambush of Varus' legions in AD 9 probably carried out with a core of turncoat German auxiliaries, who would have been similar in training and function to the legionaries themselves.

Sources:

Kagan, The Eye of Command, 2006.

Quesada Sanz, F. ‘Not so different: individual fighting techniques and small unit tactics of Roman and Iberian armies’ in P. Francois, P. Moret, S. Pere-Nogues (eds) L’Hellenisation en mediterranee occidentale au temps des guerres puniqes. Actes du Colloque International de Toulouse, 31 mars-2 avril 2005. Pallas 70 (2006) 1-25.