Is the infinitive form of verb a true verb?

My question is just as mentioned in the title of this post: Would you call an infinitive verb a true verb?

I can't find any direct mention of it anywhere on the web. The CMoS (2010) catalogs Infinitives under Verbs and defines it as follows:

An infinitive verb, also called the verb's root or stem, is a verb
that in its principal uninflected form may be preceded by to {to
dance} {to dive}.

However, chompchomp.com mentions this about infinitive verbs:

An infinitive will almost always begin with to followed by the simple
form of the verb, like this:

To + Verb = Infinitive

Important Note: Because an infinitive is not a verb, you cannot add s,
es, ed, or ing to the end. Ever!