Yes, the person who advised you that the phrases, "the way", and, "in the way", are equivalent here -- within the context of this sentence -- is correct, i.e., with either phrase, both sentences mean the very same thing. And the explanation you received from this person is correct -- for the context of this sentence.
Now, why have I twice emphasized the importance of the sentence's context? - because, the word, way, can have several different meanings depending on the context in which it is used. The previous bolded and blue highlighted word is a link to the word's entry within The American Heritage Dictionary of the English Language (Fourth Edition). Click on that link now and browse through the word's definition.
Within that entry, you will find 17 different nuanced meanings for the NOUN form of the word. Notice that, for most of these defined meanings, the entry has provided an italicized example sentence in order to illustrate that particular meaning's usage. The sixth definition -- 6. A manner or method of doing: several ways of solving this problem; had no way to reach her. -- is the one that applies to your posed sentence. Thus, the following sentences provide the very same meaning as your posed sentence:
Now, also notice that the phrase, "in the way," can be applied to the meaning of: 1b. An opening affording passage: This door is the only way into the attic. When the phrase, "in the way," is used in this context it means: blocking the passage of something, e.g., 1. The broken down car was in the way of the oncoming traffic. - or: 2a. Excuse me, but you're in the way. - or: 2b. Excuse me, but you're in my way. - meaning: ... you're blocking my passage. The IDIOMS section of the word's entry provides this explanation for this usage: in the way In a position to obstruct, hinder, or interfere.
- Measuring heart rhythms (in) the (same) way (that) a temperature is taken, this software opens a window on how a person's body handles stress.
- Measuring heart rhythms (in) the (same) manner that a temperature is taken, this software opens a window on how a person's body handles stress.
- Measuring heart rhythms using the same method as when a temperature is taken, this software opens a window on how a person's body handles stress.
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