Going off of the C17 numbering,
4/7: "A conforming program is one that is acceptable to a conforming implementation."
This definition has no restrictions regarding runtime requirements, unlike for strictly conforming programs.
5/1: "An implementation translates C source files and executes C programs in two data-processing-system environments, which will be called the translation environment and the execution environment in this International Standard. Their characteristics define and constrain the results of executing conforming C programs constructed according to the syntactic and semantic rules for conforming implementations."
So clause 5 binds all "conforming C programs constructed according to the syntactic and semantic rules for conforming implementations", not just strictly conforming programs.
Now, 4/3: "A program that is correct in all other aspects, operating on correct data, containing unspecified behavior shall be a correct program and act in accordance with 5.1.2.3."
We can interpret this as saying that "a program that is correct in all other aspects... containing unspecified behavior" is "constructed according to the syntactic and semantic rules for conforming implementations" even if it only works when "operating on correct data".
From there, it does not seem very difficult to conclude that in general, a conforming program which contains fully specified behavior, assuming it operates on correct data, is also "constructed according to the syntactic and semantic rules for conforming implementations", and is therefore bound by clause 5. If we were to instead take the negation of this conclusion, that a program is not bound by clause 5 if any possible input data causes it to violate a runtime requirement, then the wording of 4/3 would not make any sense.
(In other words, every conforming program has a corresponding set of "correct input data", and it is correct and bound by clause 5 if it does not violate any runtime requirements when given any input data within that set. A program is only incorrect if that set is empty, i.e., the UB is unconditional.)
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Meanwhile, I suppose you're looking at C++17. The note in [intro.execution]/4 is non-normative, and all of the normative language (e.g., on the very next paragraph) attaches runtime UB to the execution as a function of the input data, not the pure program.
[intro.compliance]/(2.1) and its (non-normative) footnote further clarify the distinction, stating, "If a program contains no violations of the rules in this International Standard, a conforming implementation shall, within its resource limits, accept and correctly execute that program.... 'Correct execution' can include undefined behavior, depending on the data being processed; see 1.3 and 1.9." This suggests that a program that executes undefined operations does not necessarily contain any rule violations.
