See also al-Habīr 2/292, 2/295, and Bulūgh al-Marām.
From this it becomes clear that the author’s use of the ḥadith in the present chapter is sound, unlike his use of it under “Wiping over a splint”; further clarification will come in that section.

The author states: “If a person is able to use water but fears that, by performing wuḍūʾ or ghusl, the prayer time will expire, he may perform tayammum, pray, and he is not required to repeat the prayer.”

I say: What appears to me is the opposite of that. It is established in the Sharīʿah—by the explicit text of the Quran—that tayammum is only legislated when water is unavailable. The purified Sunnah broadened the ruling to include cases of illness or severe cold, as the author himself has mentioned. But where is the evidence for permitting it when one can in fact use water?

If it is argued, “He fears the end of the prayer time,” I reply: That alone is no proof. The person who fears the lapse of time is in one of only two situations:

1. The time has become tight through his own doing—his negligence or slowness.
2. The delay was beyond his control, such as sleep or forgetfulness.

In the second situation, the time for him actually begins from the moment he wakes up or remembers, long enough for him to perform the prayer, as the Prophet ﷺ commanded in the ḥadith: “Whoever forgets a prayer or sleeps through it, its expiation is to perform it when he remembers it.” Recorded by al-Bukhārī and Muslim; the wording is Muslim’s. The Lawgiver has thus allotted this excused person a special time. When he prays as instructed, he washes for ghusl or performs wuḍūʾ with water; there is no fear of missing the time. It follows that tayammum is not permissible for him. This is the view chosen by Shaykh al-Islām Ibn Taymiyyah in al-Ikhtiyārāt, p. 12, and he cited it as the position of the majority in al-Masāʾil al-Mārdīniyyah, p. 65.

As for the first situation, it is universally accepted that, in principle, he is commanded to use water and may not resort to tayammum. Accordingly, even here he must use water; if he manages to perform the prayer on time, all well and good, and if he misses it he has only himself to blame, for he brought that outcome upon himself.

This is the conclusion that has settled my heart and given me ease, although Shaykh al-Islām and others have said that he should perform tayammum and pray. Allah knows best.

Later I noticed that al-Shawkānī seems to lean toward the view I have expressed; see al-Sayl al-Jarrār 1/126–127.